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salim-barzani

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1 years, 74 days
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These are questions asked by salim-barzani

Issue with Solving Individual Parameters...

salim-barzani 1640 Maple
type user-error
December 30 2024
1 2

When I attempt to solve for a specific parameter in Maple, it results in an error stating that the parameter does not exist. However, if I solve for all parameters, it successfully finds them, as shown in the figure. How can I resolve this issue?

parameter.mw

why taking double derivative with two di...

salim-barzani 1640 Maple 2024
differentiation physics
December 27 2024
0 6

I did a lot  of time but this time i don't know why not run any one have idea?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

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(G(xi))

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

  

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

  

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

 (2)
> 

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

xi = -V*t+x

  

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

 (3)
> 

P3 := diff(u(x, t), x, t)

``

 (4)
> 

P33 := diff(u(x, t), x)

diff(u(x, t), x)

 (5)
> 

P333 := diff(P33, t)
> 

NULL

Download why.mw

How factoring two term after substituti...

salim-barzani 1640 Maple 2024
pde differential-equations coefficients
December 27 2024
1 6

I already get the same results, but there's something about the factoring process that I encountered for the first time in this ODE. In the paper, it says that G′ satisfies a certain condition, but I’m not sure exactly what that means. Did the author use it for substitution, or did they change (m+F) into another variable and then solve? I’m not exactly sure what approach was taken. Does anyone have any idea or insight into this?

> 

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(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi))

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

  

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

  

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

  

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

 (2)
> 

tr := {t = tau, x = (-ZETA*c[3]-tau*c[4]-`Υ`*c[2]+xi)/c[1], y = `Υ`, z = ZETA, u(x, y, z, t) = U(xi)}

{t = tau, x = (-Zeta*c[3]-tau*c[4]-`Υ`*c[2]+xi)/c[1], y = `Υ`, z = Zeta, u(x, y, z, t) = U(xi)}

 (3)
> 

pde1 := diff(u(x, y, z, t), `$`(x, 3), z)-4*(diff(u(x, y, z, t), x, t))+4*(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), x, z))+2*(diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), z))+3*(diff(u(x, y, z, t), `$`(y, 2))) = 0

diff(diff(diff(diff(u(x, y, z, t), x), x), x), z)-4*(diff(diff(u(x, y, z, t), t), x))+4*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), z))+2*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), z))+3*(diff(diff(u(x, y, z, t), y), y)) = 0

 (4)
> 

``
> 

L1 := PDEtools:-dchange(tr, pde1, [xi, `Υ`, ZETA, tau, U])

(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*c[1]^3*c[3]-4*(diff(diff(U(xi), xi), xi))*c[4]*c[1]+6*(diff(U(xi), xi))*c[1]^2*(diff(diff(U(xi), xi), xi))*c[3]+3*(diff(diff(U(xi), xi), xi))*c[2]^2 = 0

 (5)
> 

map(int, (diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*c[1]^3*c[3]-4*(diff(diff(U(xi), xi), xi))*c[4]*c[1]+6*(diff(U(xi), xi))*c[1]^2*(diff(diff(U(xi), xi), xi))*c[3]+3*(diff(diff(U(xi), xi), xi))*c[2]^2 = 0, xi)

c[1]^3*c[3]*(diff(diff(diff(U(xi), xi), xi), xi))+3*c[2]^2*(diff(U(xi), xi))-4*c[4]*c[1]*(diff(U(xi), xi))+3*c[1]^2*c[3]*(diff(U(xi), xi))^2 = 0

 (6)
> 

ode := %

c[1]^3*c[3]*(diff(diff(diff(U(xi), xi), xi), xi))+3*c[2]^2*(diff(U(xi), xi))-4*c[4]*c[1]*(diff(U(xi), xi))+3*c[1]^2*c[3]*(diff(U(xi), xi))^2 = 0

 (7)
> 

F := sum(a[i]*(m+1/(diff(G(xi), xi)))^i, i = -1 .. 1)

a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

 (8)
> 

D1 := diff(F, xi)

a[-1]*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(diff(diff(G(xi), xi), xi))/(diff(G(xi), xi))^2

 (9)
> 

S := diff(G(xi), `$`(xi, 2)) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

diff(diff(G(xi), xi), xi) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

 (10)
> 

E1 := subs(S, D1)

a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2

 (11)
> 

D2 := diff(E1, xi)

2*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)-2*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)-a[-1]*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)+2*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/(diff(G(xi), xi))^3+a[1]*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/(diff(G(xi), xi))^2

 (12)
> 

E2 := subs(S, D2)

2*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)-2*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)-a[-1]*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)+2*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/(diff(G(xi), xi))^3+a[1]*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2

 (13)
> 

D3 := diff(E2, xi)

6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^4*(diff(G(xi), xi))^6)-12*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^5)-6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)+a[-1]*(2*m*mu+lambda)^2*(diff(diff(G(xi), xi), xi))/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(diff(diff(G(xi), xi), xi))/(diff(G(xi), xi))^4-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/(diff(G(xi), xi))^3-a[1]*(2*m*mu+lambda)^2*(diff(diff(G(xi), xi), xi))/(diff(G(xi), xi))^2

 (14)
> 

E3 := subs(S, D3)

6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^4*(diff(G(xi), xi))^6)-12*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^5)-6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)+a[-1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/(diff(G(xi), xi))^4-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/(diff(G(xi), xi))^3-a[1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2

 (15)
> 

NULL
> 

NULL
> 

K := U(xi) = F

U(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

 (16)
> 

K1 := diff(U(xi), xi) = E1

diff(U(xi), xi) = a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2

 (17)
> 

K2 := diff(U(xi), `$`(xi, 2)) = E2

diff(diff(U(xi), xi), xi) = 2*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)-2*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)-a[-1]*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)+2*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/(diff(G(xi), xi))^3+a[1]*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2

 (18)
> 

K3 := diff(U(xi), `$`(xi, 3)) = E3

diff(diff(diff(U(xi), xi), xi), xi) = 6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^4*(diff(G(xi), xi))^6)-12*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^5)-6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)+a[-1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/(diff(G(xi), xi))^4-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/(diff(G(xi), xi))^3-a[1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2

 (19)
> 

NULL
> 

L := eval(ode, {K, K1, K2, K3})

c[1]^3*c[3]*(6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^4*(diff(G(xi), xi))^6)-12*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^5)-6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)+a[-1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/(diff(G(xi), xi))^4-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/(diff(G(xi), xi))^3-a[1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)+3*c[2]^2*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)-4*c[4]*c[1]*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)+3*c[1]^2*c[3]*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)^2 = 0

 (20)
> 

"collect(L,(m+1/(diff(G(xi),xi))))^( )"

Error, (in collect) cannot collect m+1/diff(G(xi),xi)

  
 

NULL

Download factoring.mw

Why in two platform for ODE equation i h...

salim-barzani 1640 Maple 2024
December 24 2024
1 16

P1.mw

what is pronlem why i can't get solution...

salim-barzani 1640 Maple 2024
syntax 2dmath
December 23 2024
1 9

i already use this method for a lot of equation but this time something not normal hapening what is problem?

``

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

``
> 

eq0 := -4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0
> 

eq1 := -8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1] = 0
> 

eq2 := -4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2 = 0
> 

eq3 := 4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1] = 0
> 

eq4 := -4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2 = 0
> 

C := solve({eq0, eq1, eq2, eq3, eq4}, {a, b, c, `__ `*A[0]})

Warning, solving for expressions other than names or functions is not recommended.

  

(1)
 

NULL

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