MaplePrimes Questions

I'm trying to extract the real and imaginary parts of a given PDE. However, during the substitution step, something unexpected occurs. Specifically, my replacement does not yield the expected result, and an extra term appears: D(k)(t*w + x) in the expression P11. I'm unsure why this term arises and would appreciate any insight into what might be going wrong during the substitution process.

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, t)); declare(U(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

(2)

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), t)-beta*s*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), x)

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v+c[3]*(diff(u(x, t), t))*U(-t*v+x)^4-4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)*v+c[4]*(diff(u(x, t), t))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)+c[3]*(diff(u(x, t), x))*U(-t*v+x)^4+4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)+c[4]*(diff(u(x, t), x))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

(3)

``

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))

U(-t*v+x) = U(xi)

 

(D(U))(-t*v+x) = diff(U(xi), xi)

 

((D@@2)(U))(-t*v+x) = diff(diff(U(xi), xi), xi)

 

((D@@3)(U))(-t*v+x) = diff(diff(diff(U(xi), xi), xi), xi)

 

((D@@4)(U))(-t*v+x) = diff(diff(diff(diff(U(xi), xi), xi), xi), xi)

 

((D@@5)(U))(-t*v+x) = diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)

(4)

NULL

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k(t*w+x))

xi = -t*v+x

 

u(x, t) = U(-t*v+x)*exp(I*k(t*w+x))

(5)

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), t)-beta*s*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), x)

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v+c[3]*(diff(u(x, t), t))*U(-t*v+x)^4-4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)*v+c[4]*(diff(u(x, t), t))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)+c[3]*(diff(u(x, t), x))*U(-t*v+x)^4+4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)+c[4]*(diff(u(x, t), x))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

(6)

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(-t*v+x)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k(t*w+x))+(2*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*((D@@3)(U))(-t*v+x)*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(D(U))(-t*v+x)*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))-(24*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(D(U))(-t*v+x)*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+12*((D@@2)(U))(-t*v+x)*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(-t*v+x)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-12*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(D(U))(-t*v+x)*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+3*(D(U))(-t*v+x)*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+(4*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*((D@@3)(U))(-t*v+x)*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*((D@@2)(U))(-t*v+x)*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(D(U))(-t*v+x)*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-((D@@5)(U))(-t*v+x)*v*exp(I*k(t*w+x)))-alpha*s*c[1]*(I*U(-t*v+x)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(30*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+((D@@5)(U))(-t*v+x)*exp(I*k(t*w+x))+5*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k(t*w+x))*(D(U))(-t*v+x)*v+c[3]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(-t*v+x)^4-4*c[3]*U(-t*v+x)^4*exp(I*k(t*w+x))*(D(U))(-t*v+x)*v+c[4]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*U(-t*v+x)*exp(I*k(t*w+x))*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(I*U(-t*v+x)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(30*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+((D@@5)(U))(-t*v+x)*exp(I*k(t*w+x))+5*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k(t*w+x))*(D(U))(-t*v+x)+c[3]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(-t*v+x)^4+4*c[3]*U(-t*v+x)^4*exp(I*k(t*w+x))*(D(U))(-t*v+x)+c[4]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*U(-t*v+x)*exp(I*k(t*w+x))*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

(7)

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)NULL

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi)))

(8)

``

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0

(9)

numer(lhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))*denom(rhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0)) = numer(rhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))*denom(lhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))

-exp(I*k(t*w+x))*(-I*U(xi)*(D(k))(t*w+x)^5*c[1]*w-(4*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*c[1]*v+(6*I)*c[1]*w*(D(k))(t*w+x)^3*(diff(diff(U(xi), xi), xi))+(4*I)*c[1]*v*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-(6*I)*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))*c[1]*w-(4*I)*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))*c[1]*w+(4*I)*c[1]*v*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*c[1]*w-I*U(xi)*((D@@5)(k))(t*w+x)*c[1]*w+(6*I)*c[1]*v*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*c[1]*w+(24*I)*s*beta*U(xi)*(D(k))(t*w+x)^5-(240*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*beta*s+(240*I)*s*beta*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+(120*I)*s*beta*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))+(120*I)*s*beta*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)+(24*I)*s*beta*((D@@5)(k))(t*w+x)*U(xi)+(240*I)*s*beta*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(48*I)*U(xi)^2*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*c[4]-(48*I)*U(xi)*(diff(U(xi), xi))^2*(D(k))(t*w+x)*c[4]-(24*I)*c[2]*w*U(xi)^3*(D(k))(t*w+x)-(24*I)*c[3]*w*U(xi)^5*(D(k))(t*w+x)+24*c[1]*s*alpha*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))+48*c[4]*v*(diff(diff(diff(U(xi), xi), xi), xi))*U(xi)^2+c[1]*v*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))+24*s*beta*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))-48*c[4]*(diff(diff(diff(U(xi), xi), xi), xi))*U(xi)^2+I*c[1]*v*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))-10*c[1]*w*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-12*c[1]*v*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+18*c[1]*w*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-4*c[1]*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))+16*c[1]*w*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))+5*c[1]*w*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)+10*c[1]*w*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)+120*c[1]*s*alpha*(D(k))(t*w+x)^4*(diff(U(xi), xi))-360*c[1]*s*alpha*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-240*c[1]*s*alpha*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+192*c[4]*v*U(xi)*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+240*s*beta*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-720*s*beta*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-480*s*beta*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))-120*s*beta*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)-240*s*beta*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)-(240*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*c[1]*alpha*s-(360*I)*U(xi)*(D(k))(t*w+x)*((D@@2)(k))(t*w+x)^2*c[1]*alpha*s-(720*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*c[1]*alpha*s+240*c[1]*s*alpha*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-720*c[1]*s*alpha*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-480*c[1]*s*alpha*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))-120*c[1]*s*alpha*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)-240*c[1]*s*alpha*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)+(15*I)*c[1]*w*((D@@2)(k))(t*w+x)^2*U(xi)*(D(k))(t*w+x)+(24*I)*c[1]*s*alpha*U(xi)*(D(k))(t*w+x)^5-(240*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*c[1]*alpha*s+(240*I)*c[1]*s*alpha*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+(120*I)*c[1]*s*alpha*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))+(120*I)*c[1]*s*alpha*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)+(24*I)*c[1]*s*alpha*((D@@5)(k))(t*w+x)*U(xi)+(240*I)*c[1]*s*alpha*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(48*I)*U(xi)^2*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*c[4]*w-48*c[4]*(diff(U(xi), xi))^3-(48*I)*U(xi)*(diff(U(xi), xi))^2*(D(k))(t*w+x)*c[4]*w-(720*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*beta*s-(240*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*beta*s-(360*I)*U(xi)*(D(k))(t*w+x)*((D@@2)(k))(t*w+x)^2*beta*s-(6*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*c[1]*v+(24*I)*c[1]*w*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)^2*(diff(U(xi), xi))+(10*I)*c[1]*w*((D@@3)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^2-(24*I)*s^2*U(xi)*(D(k))(t*w+x)^2-(24*I)*c[2]*U(xi)^3*(D(k))(t*w+x)-(24*I)*c[3]*U(xi)^5*(D(k))(t*w+x)+(24*I)*w^2*U(xi)*(D(k))(t*w+x)^2+24*w^2*((D@@2)(k))(t*w+x)*U(xi)+c[1]*v*(D(k))(t*w+x)^4*(diff(U(xi), xi))-4*c[1]*w*(D(k))(t*w+x)^4*(diff(U(xi), xi))-3*c[1]*v*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))+12*c[1]*w*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-6*c[1]*v*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+4*c[1]*w*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+72*c[2]*v*U(xi)^2*(diff(U(xi), xi))+120*c[3]*v*U(xi)^4*(diff(U(xi), xi))+120*s*beta*(D(k))(t*w+x)^4*(diff(U(xi), xi))-360*s*beta*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-240*s*beta*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2-192*c[4]*U(xi)*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))-48*w*(D(k))(t*w+x)*v*(diff(U(xi), xi))-(24*I)*v^2*(diff(diff(U(xi), xi), xi))+(24*I)*s^2*(diff(diff(U(xi), xi), xi))-48*s^2*(D(k))(t*w+x)*(diff(U(xi), xi))-24*s^2*((D@@2)(k))(t*w+x)*U(xi)+48*c[4]*v*(diff(U(xi), xi))^3-72*c[2]*U(xi)^2*(diff(U(xi), xi))-120*c[3]*U(xi)^4*(diff(U(xi), xi))) = 0

(10)

%/(-exp(I*k(t*w+x)))

-()/exp(k(t*w+x)*I)

(11)
 

``

Download tr.mw

I asked similar question 5 years ago about Physics update but it was not possible to find this information

How-To-Find-What-Changed-In-Physics

I'd like to ask now again same about  SupportTools. Can one find out what update is actually included in new version?

Even if it is just 2-3 lines. It will be good if users had an idea what was fixed or improved in the new version.

Any update to software should inlcude such information. Not asking for details, just general information will be nice. Right now one does an update and have no idea at all what the new update fixed or improved which is not good.

May be such information can be displayed on screen after a user updates?

I want to convert my code output into LaTeX format, but the current formatting isn't suitable for presentation. For example, when I use simplify, it sometimes introduces unnecessary fractions, making the expression look cluttered and less elegant on paper. I'm looking for a way to simplify expressions preferably by factoring terms, without introducing extra fractions, so the final LaTeX result appears clean and well-structured.

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, t)); declare(U(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

(2)

``

RR := (2*v*(1/3)+2*alpha*beta*(1/3))*U(xi)^3+(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w)*U(xi)+(alpha*lambda+v)*(diff(diff(U(xi), xi), xi)) = 0

((2/3)*v+(2/3)*alpha*beta)*U(xi)^3+(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w)*U(xi)+(alpha*lambda+v)*(diff(diff(U(xi), xi), xi)) = 0

(3)

IM := -2*(diff(diff(U(xi), xi), xi))*v*k-2*U(xi)*k^2*w^2-2*(diff(diff(U(xi), xi), xi))*alpha^2+2*(diff(diff(U(xi), xi), xi))*v^2+(diff(diff(U(xi), xi), xi))*k*w+2*U(xi)^3*k*w-2*U(xi)^3*alpha*beta*k-3*(diff(diff(U(xi), xi), xi))*alpha*k*lambda-U(xi)*k^3*w+2*U(xi)*alpha^2*k^2+U(xi)*alpha*k^3*lambda = 0

-2*(diff(diff(U(xi), xi), xi))*v*k-2*U(xi)*k^2*w^2-2*(diff(diff(U(xi), xi), xi))*alpha^2+2*(diff(diff(U(xi), xi), xi))*v^2+(diff(diff(U(xi), xi), xi))*k*w+2*U(xi)^3*k*w-2*U(xi)^3*alpha*beta*k-3*(diff(diff(U(xi), xi), xi))*alpha*k*lambda-U(xi)*k^3*w+2*U(xi)*alpha^2*k^2+U(xi)*alpha*k^3*lambda = 0

(4)

collect(%, {U(xi), diff(diff(U(xi), xi), xi)})

(-2*alpha*beta*k+2*k*w)*U(xi)^3+(alpha*k^3*lambda+2*alpha^2*k^2-k^3*w-2*k^2*w^2)*U(xi)+(-3*alpha*k*lambda-2*alpha^2-2*k*v+k*w+2*v^2)*(diff(diff(U(xi), xi), xi)) = 0

(5)

P := %

(-2*alpha*beta*k+2*k*w)*U(xi)^3+(alpha*k^3*lambda+2*alpha^2*k^2-k^3*w-2*k^2*w^2)*U(xi)+(-3*alpha*k*lambda-2*alpha^2-2*k*v+k*w+2*v^2)*(diff(diff(U(xi), xi), xi)) = 0

(6)

NULL

NULL

C1 := v = solve(2*v*(1/3)+2*alpha*beta*(1/3) = 0, v)

v = -alpha*beta

(7)

C2 := k = solve(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w = 0, k)

k = (0, -4*(alpha^2+v*w)/(3*alpha*lambda+v-2*w))

(8)

C22 := subs(C1, C2)

k = (0, -4*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w))

(9)

C222 := k = -(4*(-alpha*beta*w+alpha^2))/(-alpha*beta+3*alpha*lambda-2*w)

k = -4*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)

(10)

ode := subs({C1, C222}, P)

(8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0

(11)

numer(lhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))*denom(rhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0)) = numer(rhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))*denom(lhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))

-2*alpha*(-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w+24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3+4*U(xi)^3*alpha^4*beta^3-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4) = 0

(12)

simplify(-2*alpha*(24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+4*U(xi)^3*alpha^4*beta^3+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4) = 0)

-64*alpha*((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi)) = 0

(13)

%/(-64*alpha)

(1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0

(14)

PP := numer(lhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))*denom(rhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0)) = numer(rhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))*denom(lhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))

-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w+24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3+4*U(xi)^3*alpha^4*beta^3-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4 = 0

(15)

NULL

collect(PP, {U(xi), diff(U(xi), xi), diff(diff(U(xi), xi), xi)})

(-4*alpha^3*beta^4*w+24*alpha^3*beta^3*lambda*w-36*alpha^3*beta^2*lambda^2*w+4*alpha^4*beta^3-24*alpha^4*beta^2*lambda+36*alpha^4*beta*lambda^2-12*alpha^2*beta^3*w^2+24*alpha^2*beta^2*lambda*w^2+36*alpha^2*beta*lambda^2*w^2+12*alpha^3*beta^2*w-24*alpha^3*beta*lambda*w-36*alpha^3*lambda^2*w-48*alpha*beta*lambda*w^3+48*alpha^2*lambda*w^2+16*beta*w^4-16*alpha*w^3)*U(xi)^3+(32*alpha^3*beta^3*lambda*w^3-16*alpha^4*beta^3*w^2-48*alpha^4*beta^2*lambda*w^2-16*alpha^2*beta^3*w^4-48*alpha^2*beta^2*lambda*w^4+32*alpha^5*beta^2*w+32*alpha^3*beta^2*w^3+96*alpha^3*beta*lambda*w^3+32*alpha*beta^2*w^5-16*alpha^6*beta+16*alpha^6*lambda-16*alpha^4*beta*w^2-48*alpha^4*lambda*w^2-64*alpha^2*beta*w^4+32*alpha^3*w^3)*U(xi)+(-alpha^4*beta^5+9*alpha^4*beta^4*lambda-27*alpha^4*beta^3*lambda^2+27*alpha^4*beta^2*lambda^3-2*alpha^3*beta^4*w+6*alpha^3*beta^3*lambda*w+18*alpha^3*beta^2*lambda^2*w-54*alpha^3*beta*lambda^3*w-3*alpha^4*beta^3+21*alpha^4*beta^2*lambda-45*alpha^4*beta*lambda^2+27*alpha^4*lambda^3+6*alpha^2*beta^3*w^2-48*alpha^2*beta^2*lambda*w^2+90*alpha^2*beta*lambda^2*w^2-12*alpha^3*beta^2*w+48*alpha^3*beta*lambda*w-36*alpha^3*lambda^2*w+16*alpha*beta^2*w^3-48*alpha*beta*lambda*w^3-12*alpha^2*beta*w^2+12*alpha^2*lambda*w^2+8*beta*w^4)*(diff(diff(U(xi), xi), xi)) = 0

(16)
 

NULL

Download B-R.mw

How can we eliminate nonlinear terms involving two functions in a differential equation?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(G(xi)); declare(Q(x, t)); declare(Q1(x, t))

G(xi)*`will now be displayed as`*G

 

Q(x, t)*`will now be displayed as`*Q

 

Q1(x, t)*`will now be displayed as`*Q1

(2)

NULL

q := (sqrt(P)+Q(x, t))*exp(I*gamma*P*t); B := (sqrt(P)+Q(x, t))*exp(-I*gamma*P*t); B1 := sqrt(P)+Q(x, t); P+sqrt(P)*(Q1(x, t)+Q(x, t))

GeF := I*(diff(q, t))+alpha[1]*(diff(q, x, x))+alpha[2]*(P+sqrt(P)*(Q1(x, t)+Q(x, t)))*q+alpha[3]*(P+sqrt(P)*(Q1(x, t)+Q(x, t)))^2*q+alpha[4]*(P+sqrt(P)*(Q1(x, t)+Q(x, t)))^3*q+alpha[5]*(diff(P+sqrt(P)*(Q1(x, t)+Q(x, t)), x, x))*q = 0

K := simplify(GeF*exp(-I*gamma*P*t))

(Q(x, t)^4*alpha[4]+3*Q(x, t)^3*Q1(x, t)*alpha[4]+3*(Q1(x, t)^2*alpha[4]+alpha[3])*Q(x, t)^2+Q1(x, t)*(Q1(x, t)^2*alpha[4]+4*alpha[3])*Q(x, t)+Q1(x, t)^2*alpha[3]+alpha[2]-gamma)*P^(3/2)+(6*Q(x, t)^2*alpha[4]+9*Q(x, t)*Q1(x, t)*alpha[4]+3*Q1(x, t)^2*alpha[4]+alpha[3])*P^(5/2)+(P^(1/2)*Q(x, t)*alpha[5]+P*alpha[5]+alpha[1])*(diff(diff(Q(x, t), x), x))+alpha[5]*(P^(1/2)*Q(x, t)+P)*(diff(diff(Q1(x, t), x), x))+P^(7/2)*alpha[4]+I*(diff(Q(x, t), t))+alpha[2]*(Q1(x, t)*Q(x, t)+Q(x, t)^2)*P^(1/2)+(4*P^2*alpha[4]+P*alpha[3])*Q(x, t)^3+(9*P^2*alpha[4]+2*P*alpha[3])*Q1(x, t)*Q(x, t)^2+((6*P^2*alpha[4]+P*alpha[3])*Q1(x, t)^2+4*alpha[4]*P^3+3*alpha[3]*P^2+(2*alpha[2]-gamma)*P)*Q(x, t)+P^2*Q1(x, t)^3*alpha[4]+(3*P^3*alpha[4]+2*P^2*alpha[3]+P*alpha[2])*Q1(x, t) = 0

(3)

remove(has, K, {Q(x, t)^2, Q(x, t)^3, Q(x, t)^4, Q1(x, t)^2, Q1(x, t)^3, Q1(x, t)^4})

() = 0

(4)

NULL

NULL

AA := (alpha[2]-gamma)*P^(3/2)+alpha[3]*P^(5/2)+(P*alpha[5]+alpha[1])*(diff(Q(x, t), x, x))+alpha[5]*P*(diff(Q1(x, t), x, x))+P^(7/2)*alpha[4]+I*(diff(Q(x, t), t))+(4*alpha[4]*P^3+3*alpha[3]*P^2+(2*alpha[2]-gamma)*P)*Q(x, t)+(3*P^3*alpha[4]+2*P^2*alpha[3]+P*alpha[2])*Q1(x, t) = 0

(alpha[2]-gamma)*P^(3/2)+P^(5/2)*alpha[3]+(P*alpha[5]+alpha[1])*(diff(diff(Q(x, t), x), x))+P*(diff(diff(Q1(x, t), x), x))*alpha[5]+P^(7/2)*alpha[4]+I*(diff(Q(x, t), t))+(4*alpha[4]*P^3+3*alpha[3]*P^2+(2*alpha[2]-gamma)*P)*Q(x, t)+(3*P^3*alpha[4]+2*P^2*alpha[3]+P*alpha[2])*Q1(x, t) = 0

(5)
 

test := (alpha[2]-gamma)*P^(3/2)+alpha[3]*P^(5/2)+(P*alpha[5]+alpha[1])*0+P*alpha[5]*0+P^(7/2)*alpha[4]+I*0 = 0

(alpha[2]-gamma)*P^(3/2)+P^(5/2)*alpha[3]+P^(7/2)*alpha[4] = 0

(6)
 

NULL

Download remove.mw

Hi!

Sorry if I am missing something or not following any implicit rules, I am really new to Maple and this forum.

For the sake of completeness, here the code that is given:

Ve := Vector([VeX, VeY, VeZ]);
with(LinearAlgebra);
Vh := Normalize(Vector([alphaX*Ve(1), alphaY*Ve(2), Ve(3)]), Euclidean, conjugate = false);
lensq := Vh(1)*Vh(1) + Vh(2)*Vh(2);
T1 := Vector([-Vh(2), Vh(1), 0])/sqrt(lensq);
T2 := CrossProduct(Vh, T1);
r := sqrt(x);
phi := 2*Pi*y;
t1 := r*cos(phi);
t2 := r*sin(phi);
s := 1/2*(1 + Vh(3));
t22 := (1 - s)*sqrt(1 - t1*t1) + s*t2;
Nh := t1*T1 + t22*T2 + sqrt(1 - t1*t1 - t22*t22)*Vh;
NULL;
Ne := Normalize(Vector([alphaX*Nh(1), alphaY*Nh(2), Nh(3)]), Euclidean, conjugate = false);
AV := (-1 + sqrt(1 + (alphaX^2*Ve(1)^2 + alphaY^2*Ve(2)^2)/Ve(3)^2))/2;
G1 := 1/(1 + AV);
DN := 1/(Pi*alphaX*alphaY*(Ne(1)^2/alphaX^2 + Ne(2)^2/alphaY^2 + Ne(3)^2)^2);

DVN := G1*DotProduct(Ve, Ne, conjugate = false)*DN/DotProduct(Ve, Vector([0, 0, 1]), conjugate = false);
PDF := DVN/(4*DotProduct(Ve, Ne, conjugate = false));

 

So far, so good. Now what I want to do is:

PDFint := int(PDF, [x = xInf .. xSup, y = yInf .. ySup]);

to calculate the symbolic integral of PDF over x and y. The issue is that I keep running out of memory after a few hours and my operating system (Linux Fedora) automatically shuts Maple down.

I am convinced that there must be a way to either preprocess PDF so that the int(...) command doesn't eat up all the RAM, or some different way to calculate an integral that maybe has a different structure?

I have tried codegen[optimize](PDF) and liked what it did, but I don't know how to progress with the result of it, if at all possible.

I know that there is also a way to calculate the integral numerically, but I need the analytic integral, so numerical solutions are of no use to me.

If there is really no way for me to obtain this integral, I would really appreciate an explanation of why, so that I can rest at night finally lol.

Thank you in advance,

Jane

I’ve successfully plotted this exercise, but I’m exploring ways to improve the visualization. Specifically, I’d like to know if it's possible to combine a 2D plot as a smaller inset within a 3D plot, positioned in a corner of the 3D graph.

Additionally, I’ve noticed that although the same data is plotted in different examples, the design and style of the plots can vary significantly, some look much more polished or professional. Are there recommended techniques, functions, or toolboxes in Maple that can help improve the visual design or aesthetic of the plots

Download plot.mw

Yes , i can ..a procedure for thiis?

restart; with(plots); printf("Step 1: Declare l and b as free variables for the 3D plot.\n"); l := 'l'; b := 'b'; printf("Step 2: Set fixed values for remaining parameters.\n"); a := 1; c := 1; d := .2; f := 1; epsilon := 1; printf("Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.\n"); G := proc (l, b) options operator, arrow; 2*Im(sqrt(-a^2*f*d-a*b+(1/2)*l^2-3*a+(1/2)*sqrt(-48*a^3*f*d+4*epsilon*l^3*c-24*a*epsilon*l*c+l^4+4*l^2*c^2-48*a^2*b-12*a*l^2+36*a^2))) end proc; printf("Step 4: Create a 3D surface plot of G(l,b).\n"); gainPlot := plot3d(G(l, b), l = -6 .. 4, b = .1 .. 1.2, labels = ["Wave number l", "Parameter b", "Gain G(l,b)"], title = "3D MI Gain Spectrum over (l, b)", shading = zhue, axes = boxed, grid = [60, 60]); printf("Step 5: Display the 3D surface plot.\n"); gainPlot

Step 1: Declare l and b as free variables for the 3D plot.
Step 2: Set fixed values for remaining parameters.
Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.
Step 4: Create a 3D surface plot of G(l,b).
Step 5: Display the 3D surface plot.

 

 
 

 

Download can_we_plotthisin_3Dshapemprimes5-5-2025.mw

in here How we can seperate the coefficent of conjugate this conjugate sign how remove from my equation ?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, t)); declare(U(xi)); declare(V(xi)); declare(P(x, t)); declare(q(x, t))

u(x, t)*`will now be displayed as`*u

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

 

P(x, t)*`will now be displayed as`*P

 

q(x, t)*`will now be displayed as`*q

(2)

pde := I*(diff(u(x, t), t))+diff(u(x, t), `$`(x, 2))+abs(u(x, t))^2*u(x, t) = 0

I*(diff(u(x, t), t))+diff(diff(u(x, t), x), x)+abs(u(x, t))^2*u(x, t) = 0

(3)

S := u(x, t) = (sqrt(a)+P(x, t))*exp(I*a*t)

u(x, t) = (a^(1/2)+P(x, t))*exp(I*a*t)

(4)

S1 := conjugate(u(x, t)) = (sqrt(a)+conjugate(P(x, t)))*exp(-I*a*t)

conjugate(u(x, t)) = (a^(1/2)+conjugate(P(x, t)))*exp(-I*a*t)

(5)

Q := abs(u(x, t))^2 = u(x, t)*conjugate(u(x, t))

abs(u(x, t))^2 = u(x, t)*conjugate(u(x, t))

(6)

F1 := expand(simplify(subs({S, S1}, rhs(Q))))

a+a^(1/2)*P(x, t)+a^(1/2)*conjugate(P(x, t))+abs(P(x, t))^2

(7)

F2 := abs(u(x, t))^2 = remove(has, F1, abs(P(x, t))^2)

abs(u(x, t))^2 = a+a^(1/2)*P(x, t)+a^(1/2)*conjugate(P(x, t))

(8)

FF := collect(F2, sqrt(a))

abs(u(x, t))^2 = a+(P(x, t)+conjugate(P(x, t)))*a^(1/2)

(9)

F3 := abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*sqrt(a))*rhs(S)

abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*a^(1/2))*(a^(1/2)+P(x, t))*exp(I*a*t)

(10)

F4 := remove(has, F3, P(x, t)*conjugate(P(x, t)))

abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*a^(1/2))*(a^(1/2)+P(x, t))*exp(I*a*t)

(11)

expand(%)

abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a^(1/2)*P(x, t)^2+exp(I*a*t)*a*conjugate(P(x, t))+exp(I*a*t)*a^(1/2)*conjugate(P(x, t))*P(x, t)

(12)

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, P(x, t) = T*P(x, t)))/T, T) end proc, expand(%))

() = (), abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a^(1/2)*P(x, t)^2+exp(I*a*t)*a*conjugate(P(x, t))+exp(I*a*t)*a^(1/2)*conjugate(P(x, t))*P(x, t)

(13)

F6 := abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a*conjugate(P(x, t))

abs(u(x, t))^2*u(x, t) = exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t))

(14)

subs({F6, S}, pde)

I*(diff((a^(1/2)+P(x, t))*exp(a*t*I), t))+diff(diff((a^(1/2)+P(x, t))*exp(a*t*I), x), x)+exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

(15)

eval(%)

I*((diff(P(x, t), t))*exp(a*t*I)+I*(a^(1/2)+P(x, t))*a*exp(a*t*I))+(diff(diff(P(x, t), x), x))*exp(a*t*I)+exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

(16)

expand(%)

I*(diff(P(x, t), t))*exp(a*t*I)+exp(a*t*I)*a*P(x, t)+(diff(diff(P(x, t), x), x))*exp(a*t*I)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

(17)

expand(%/exp(I*a*t))

I*(diff(P(x, t), t))+a*P(x, t)+diff(diff(P(x, t), x), x)+a*conjugate(P(x, t)) = 0

(18)

PP := collect(%, a)

(P(x, t)+conjugate(P(x, t)))*a+I*(diff(P(x, t), t))+diff(diff(P(x, t), x), x) = 0

(19)

U1 := P(x, t) = r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))

P(x, t) = r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))

(20)

eval(subs(U1, PP))

(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))+conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))))*a+I*(-I*r[1]*m*exp(I*(l*x-m*t))+I*r[2]*m*exp(-I*(l*x-m*t)))-r[1]*l^2*exp(I*(l*x-m*t))-r[2]*l^2*exp(-I*(l*x-m*t)) = 0

(21)

simplify((r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))+conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))))*a+I*(-I*r[1]*m*exp(I*(l*x-m*t))+I*r[2]*m*exp(-I*(l*x-m*t)))-r[1]*l^2*exp(I*(l*x-m*t))-r[2]*l^2*exp(-I*(l*x-m*t)) = 0)

conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t)))*a+r[2]*(-l^2+a-m)*exp(-I*(l*x-m*t))+r[1]*exp(I*(l*x-m*t))*(-l^2+a+m) = 0

(22)

J := eval(%)

conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t)))*a+r[2]*(-l^2+a-m)*exp(-I*(l*x-m*t))+r[1]*exp(I*(l*x-m*t))*(-l^2+a+m) = 0

(23)

expand(%)

a*conjugate(r[1])*exp(I*conjugate(m)*conjugate(t))/exp(I*conjugate(l)*conjugate(x))+a*conjugate(r[2])*exp(I*conjugate(l)*conjugate(x))/exp(I*conjugate(m)*conjugate(t))-r[2]*exp(I*m*t)*l^2/exp(I*l*x)+r[2]*exp(I*m*t)*a/exp(I*l*x)-r[2]*exp(I*m*t)*m/exp(I*l*x)-r[1]*exp(I*l*x)*l^2/exp(I*m*t)+r[1]*exp(I*l*x)*a/exp(I*m*t)+r[1]*exp(I*l*x)*m/exp(I*m*t) = 0

(24)

indets(%)

{a, l, m, t, x, r[1], r[2], exp(I*l*x), exp(I*m*t), exp(I*conjugate(l)*conjugate(x)), exp(I*conjugate(m)*conjugate(t)), conjugate(l), conjugate(m), conjugate(t), conjugate(x), conjugate(r[1]), conjugate(r[2])}

(25)

subs({exp(-I*(l*x-m*t)) = Y, exp(I*(l*x-m*t)) = X}, J)

conjugate(X*r[1]+Y*r[2])*a+r[2]*(-l^2+a-m)*Y+r[1]*X*(-l^2+a+m) = 0

(26)

collect(%, {X, Y})

conjugate(X*r[1]+Y*r[2])*a+r[2]*(-l^2+a-m)*Y+r[1]*X*(-l^2+a+m) = 0

(27)

Download conjugate.mw

according to what is new in Maple 2025, it says

  • Maple 2025 introduces several important improvements to simplify regarding expressions containing exponential, trigonometric, hyperbolic, and/or inverse trigonometric functions, resulting in more compact results. Other commands in the math library also provide simpler results due to these improvements.

But I still see weakness in simplify. (see also recent question).

Here is an example, A and B below are equivalent mathematically. But A is almost twice as big. So one would expect simplify(A) to return B. right? But it does not. Also using size option has no effect.  

Does one need more tricks in Maple to make it simplify this? Is this not something that a powerful CAS software like Maple should have been able to do?

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`


A:=(-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4;
B:=(4*exp(x/2)-x-2)^2;

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(4*exp((1/2)*x)-x-2)^2

#check leaf size
MmaTranslator:-Mma:-LeafCount(A);

22

MmaTranslator:-Mma:-LeafCount(B);

13

#check they are the same
simplify(A-B);

0

#then why Maple can not simplify A to B ??
simplify(A);
simplify(A,size);
simplify(A,size,exp);
simplify(A) assuming real;

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

Student:-Precalculus:-CompleteSquare(A)

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

 

 

Download why_can_not_simplify_may_4_2025.mw

Using another software, all what is needed is call to Simpify to do it:

I also tried my most power full_simplify() function in Maple, and it had no effect

full_simplify:=proc(e::anything)
   local result::list;
   local f:=proc(a,b)
      RETURN(MmaTranslator:-Mma:-LeafCount(a)<MmaTranslator:-Mma:-LeafCount(b))
   end proc;

   #add more methods as needed

   result:=[simplify(e),
            simplify(e,size),
            simplify(combine(e)),
            simplify(combine(e),size),
            radnormal(evala( combine(e) )),
            simplify(evala( combine(e) )),
            evala(radnormal( combine(e) )),
            simplify(radnormal( combine(e) )),
            evala(factor(e)),
            simplify(e,ln),
            simplify(e,power),
            simplify(e,RootOf),
            simplify(e,sqrt),
            simplify(e,trig),
            simplify(convert(e,trig)),
            simplify(convert(e,exp)),
            combine(e)
   ];   
   RETURN( sort(result,f)[1]);   

end proc:

Calling full_simplify(A) did not simplify it.

I wanted to search for all files with some extention in directory tree. But when adding depth=infinity and also adding 'select'="*.log" (or whatever the extension I want is), then it returns an empty list even though there are files with this extension but deep in the tree.

If I remove select, then it does work, but it returns list of the files in the tree. Which I do not want. I want to filter these by select.

If I remove depth=infinity then select works but only finds such files at top level of the directory and does look down the tree where there are more such files.

It seems select and depth conflict with each others.  Adding 'all' option makes no difference.

I do not remember now if I reported this before or not.

Here is worksheet showing this problem

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

folder_name:="/home/me/maple2025"; #fails to find all such files
FileTools:-ListDirectory(folder_name,'select'="*.wav",depth=infinity);

"/home/me/maple2025"

[]

folder_name:="/home/me/maple2025"; #works but only top level
FileTools:-ListDirectory(folder_name,'select'="*.log");

"/home/me/maple2025"

["Maple_2025_Install_2025_04_03_12_34_10.log"]

folder_name:="/home/me/maple2025"; #works but this finds everything
FileTools:-ListDirectory(folder_name,depth=infinity);

"/home/me/maple2025"

`[Length of output exceeds limit of 10000]`

 


 

Download listdirectory_may_3_2025.mw

How can one get list of files with specific extension in the whole tree? And why is adding select makes it not work? Help does not say anything about select does not work when adding depth=infinity.

I suppose I can get list of all files in tree, then iterate over the list and remove all entries that do not end with the extension I wanted. But this is what select is supposed to do. For example

folder_name:="/home/me/maple2025/"; #works but this finds everything
L:=FileTools:-ListDirectory(folder_name,depth=infinity):
map(X->`if`(FileTools:-Extension(X)="wav",X,NULL),L);

Gives list of only files with extension "wav". So the above is workaround for now.

I’m currently trying to collect terms in an expression f^G(xi), but the result is not behaving as expected. I attempted two different coding approaches, but both resulted in errors. This particular case of collecting terms seems to be different from what I’ve encountered before, and I’m unsure how to resolve it.

Could you please advise on how to properly collect the terms in this situation and avoid the errors? Any insight into why this case behaves differently would also be appreciated.

Thank you for your help.

collect_term.mw

I am currently working with an ordinary differential equation (ODE) that I find difficult to express and solve accurately. In this ODE, the symbol f represents an exponential function rather than a typical variable, which adds to the confusion. Although I have followed the format used in related research papers, the results I obtain are not satisfactory.

Since this type of ODE is new and somewhat unfamiliar to me, I would greatly appreciate your guidance in:

  1. Properly formulating the ODE.

  2. Understanding the role of f in the context of exponential functions.

  3. Finding the correct and complete solutions.

  4. Learning how to clearly present each solution step by step.

Thank you in advance for your support.

AA.mw

These are the same (i.e. mathematically equivalent for real x)

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

But can't see how to use Maple to show this, other than numerically and by plotting.

Any one knows of a trick? Below is worksheet. Using another software, it was able to show they are same:

Here are my attempts in Maple 2025
 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

restart;

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

-x*(x-4*exp((1/2)*x)+2)

x*((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)

plots:-display(Array([plot(A,x=-3..3),plot(B,x=-3..3)]))

 

 

Digits:=16;
seq(MmaTranslator:-Mma:-Chop(A-B),x=-2..2,.1)

16

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

simplify(A-B);

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(A-B) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(evala(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(normal(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(A-B,exp) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(evalc(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

 

 

Download show_same_may_3_2025.mw

Manually factoring each equation in this system one by one is time-consuming and inefficient. Is there a way to automate the factoring of expressions into two multiplicative terms—some of which may be single-term factors—using code?

restart

with(PDEtools)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

G1 := 5*lambda^2*alpha[1]^4*alpha[0]*a[4]+lambda^2*alpha[1]^4*a[3]-10*lambda*alpha[1]^2*alpha[0]^3*a[4]+lambda*k^2*a[1]*alpha[1]^2-6*lambda*alpha[1]^2*alpha[0]^2*a[3]+alpha[0]^5*a[4]-k^2*a[1]*alpha[0]^2-3*lambda*alpha[1]^2*alpha[0]*a[2]+alpha[0]^4*a[3]+lambda*w*alpha[1]^2+alpha[0]^3*a[2]-w*alpha[0]^2+((lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1])*(diff(G(xi), xi))+lambda^2*beta[0]*a[5]*alpha[1]^2-4*mu*lambda*alpha[1]^4*a[3]+5*lambda^2*beta[0]*alpha[1]^4*a[4]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]+12*mu*alpha[1]^2*alpha[0]^2*a[3]+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*lambda*alpha[1]^2*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*lambda*alpha[1]^2*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3]-2*w*alpha[0]*beta[0]+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*mu*w*alpha[1]^2)/G(xi)+((1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-k^2*a[1]*beta[0]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-9*mu^2*alpha[1]^2*a[1]*(1/4)-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]-(1/4)*lambda*beta[0]^2*a[1]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-20*mu*lambda*beta[0]*alpha[1]^4*a[4]-7*mu*lambda*beta[0]*a[5]*alpha[1]^2+(2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-4*lambda*beta[0]*alpha[1]^3*a[3]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4]-mu*lambda*alpha[1]^3*a[5]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]-2*k^2*a[1]*alpha[1]*beta[0]-(1/2)*lambda*beta[0]*alpha[1]*a[1]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))-w*beta[0]^2)/G(xi)^2+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+3*beta[0]^2*alpha[1]*a[2]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)+8*mu*beta[0]*alpha[1]^3*a[3]-2*lambda*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]-6*mu^2*alpha[1]^3*a[5]-10*lambda*beta[0]^2*alpha[1]^3*a[4]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+beta[0]^3*a[2]-14*mu^2*beta[0]*a[5]*alpha[1]^2+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+mu*beta[0]^2*a[1]-lambda*beta[0]^3*a[5]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3])/G(xi)^3+((4*beta[0]^3*alpha[1]*a[3]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^3*a[5]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+20*mu*beta[0]^2*alpha[1]^3*a[4]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+20*mu*beta[0]^3*alpha[1]^2*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*alpha[1]^4*a[4]+beta[0]^4*a[3]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+3*mu*beta[0]^3*a[5]+5*beta[0]^4*alpha[0]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4))/G(xi)^4+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5]+5*beta[0]^4*alpha[1]*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4])*(diff(G(xi), xi))+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+beta[0]^5*a[4])/G(xi)^5 = 0

indets(G1)

{k, lambda, mu, w, xi, B[1], B[2], a[1], a[2], a[3], a[4], a[5], alpha[0], alpha[1], beta[0], G(xi), diff(G(xi), xi)}

(2)

``

(3)

eq0 := 5*lambda^2*a[4]*alpha[0]*alpha[1]^4+lambda^2*a[3]*alpha[1]^4-10*lambda*a[4]*alpha[0]^3*alpha[1]^2+k^2*lambda*a[1]*alpha[1]^2-6*lambda*a[3]*alpha[0]^2*alpha[1]^2+a[4]*alpha[0]^5-k^2*a[1]*alpha[0]^2-3*lambda*a[2]*alpha[0]*alpha[1]^2+a[3]*alpha[0]^4+lambda*w*alpha[1]^2+a[2]*alpha[0]^3-w*alpha[0]^2 = 0

``

eq1 := lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1] = 0

eq2 := lambda^2*beta[0]*a[5]*alpha[1]^2+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*alpha[1]^2*lambda*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]+12*mu*alpha[1]^2*alpha[0]^2*a[3]-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2+5*lambda^2*beta[0]*alpha[1]^4*a[4]-4*mu*lambda*alpha[1]^4*a[3]-2*mu*w*alpha[1]^2+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*w*alpha[0]*beta[0]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3] = 0

NULL

eq3 := (1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]-9*mu^2*alpha[1]^2*a[1]*(1/4)-w*beta[0]^2+3*beta[0]^2*alpha[0]*a[2]-(1/4)*lambda*beta[0]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4] = 0

eq4 := 2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0]-2*k^2*a[1]*alpha[1]*beta[0]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]-4*lambda*beta[0]*alpha[1]^3*a[3]-lambda*alpha[1]^3*mu*a[5]-(1/2)*lambda*beta[0]*alpha[1]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4] = 0

eq5 := -6*mu^2*alpha[1]^3*a[5]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+3*beta[0]^2*alpha[1]*a[2]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+8*mu*beta[0]*alpha[1]^3*a[3]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)-10*lambda*beta[0]^2*alpha[1]^3*a[4]-2*lambda*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5] = 0

eq6 := -14*mu^2*beta[0]*a[5]*alpha[1]^2+beta[0]^3*a[2]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3]-lambda*beta[0]^3*a[5]+mu*beta[0]^2*a[1]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4] = 0

eq7 := 4*beta[0]^3*alpha[1]*a[3]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*mu*a[5]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+20*mu*beta[0]^2*alpha[1]^3*a[4]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4] = 0

eq8 := 4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+beta[0]^4*a[3]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+20*mu*beta[0]^3*alpha[1]^2*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4)+5*beta[0]^4*alpha[0]*a[4]+3*mu*beta[0]^3*a[5]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*alpha[1]^4*a[4] = 0

eq9 := (10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+5*beta[0]^4*alpha[1]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5] = 0

eq10 := (2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+beta[0]^5*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4] = 0

 

with(LargeExpressions)

COEFFS := solve({eq0, eq1, eq10, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {w, a[1], a[2], alpha[0], alpha[1], beta[0]})

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