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why get Error when do seperet real and i...

salim-barzani 1555 Maple 2021
syntax 2dmath differential-equations
October 12 2024
2 2

each time i use this i did not have any problem but this equation not seperate any one know what is problem?

> 

restart
> 

with(SolveTools)
> 

undeclare(prime)

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

 (1)
> 

with(PDEtools)
> 

P := U(xi)^3*mu*C[2]*h[9]+(2*I)*(diff(U(xi), xi))*a*k*mu+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]-(4*(diff(U(xi), xi))*I)*k*mu^3*h[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]*I+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+2*(0+I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

U(xi)^3*mu*C[2]*h[9]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v+(2*I)*(diff(U(xi), xi))*a*k*mu-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

 (2)
> 

Re(P)

Re(U(xi)^3*mu*C[2]*h[9]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)))-Im((diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+U(xi)*mu^4*C[2]*h[7]-(diff(U(xi), xi))*v+2*(diff(U(xi), xi))*a*k*mu+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]) = 0

 (3)
 

``

Download real_and_imaginary_.mw

Transformation of strange equation In PD...

salim-barzani 1555 Maple 2021
pde differential-equations
October 11 2024
0 0

I have  a big problem in transformation How we can do suh transformation in  type of  procure  without use any hand work for example in physic abs|-| remove the exponential term how the maple remove that term automatically and collect all term and do my transformation this example is really hard one which is must do a lot by hand and mixed them which maybe a week take my time to get results and how i reach the results without spending that time i have a result of this equation and i am try to get but i don't know the results of this person is correct or not but i will share in here,  i did some try i will share in here too if in DEchange add U(xi) it will work and give me the other step but i need something more effective, when q^* is conjugate of q =exp(-ipsi(x,t))U(xi)

> 

NULL
> 

restart
> 

with(PDEtools)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

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

 (1)

 

 
> 

tr := {t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

{t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

 (2)
> 

pde := I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(u(x, t), `$`(x, 2)))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(u(x, t), `$`(x, 4)))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(u(x, t), `$`(x, 2)))+h[5]*u(x, t)^2*(diff(u[1](x, t), `$`(x, 2)))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(u(x, t), `$`(x, 4)))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(diff(u(x, t), x), x))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(diff(u(x, t), x), x))+h[5]*u(x, t)^2*(diff(diff(u[1](x, t), x), x))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

 (3)
> 

``
> 

PDEtools:-dchange(tr, pde, [xi, tau, U, U(xi)])

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+b*U(xi)^3*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+C[1](h[1]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[2]*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)^2*k^2*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[3]*abs((exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k)^2*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[4]*U(xi)^2*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[5]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(diff(U(xi), xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-(2*I)*(diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k-U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[6]*U(xi)^5*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))+I*C[2]*(h[7]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[8]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k+h[9]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-I*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k) = 0

 (4)
 

NULL


Download find_ODE.mw

3D plot, Matlab export...

salim-barzani 1555 Maple 2021
October 05 2024
3 16

Hi

How merge or combine two or more 3D plot together ? and How many 3D plot exist for describe graph ? and how we can transfer this combine plot to another program like matlab?

Maple is  good for decribe plot  and very faster from other program but for visualization and some other stuff we need other language program, so how we can combine the plot and how we transfer this plot another program like matlab i know the matlab have special template for this kind plot but i didn't have the template if any one have it it will be  awesome?

Download combine_graph.mw

When i do substitute in equation two par...

salim-barzani 1555 Maple 2021
ode substitution differential-equations
September 30 2024
1 3

how fixed this for ode test

> 

restart
> 

with(PDEtools)
> 

with(Physics)
> 

undeclare(prime)

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

 (1)
> 

``
> 

pde := -I*(diff(U(xi), xi))*gamma*k*mu+I*gamma*(diff(U(xi), xi))*sigma*w+(diff(diff(U(xi), xi), xi))*gamma*k*w+U(xi)*gamma*mu*sigma+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*w-U(xi)*sigma^2-U(xi)*mu

-I*gamma*(diff(U(xi), xi))*k*mu+I*gamma*(diff(U(xi), xi))*sigma*w+gamma*(diff(diff(U(xi), xi), xi))*k*w+gamma*U(xi)*mu*sigma+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*w-U(xi)*sigma^2-U(xi)*mu

 (2)
> 

case1 := [mu = -(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1), A[0] = 0, A[1] = -RootOf(_Z^2*alpha+gamma*k*w+k^2), B[1] = RootOf(_Z^2*alpha+gamma*k*w+k^2), w = (gamma*k*mu-2*k*sigma)/(gamma*sigma-1)]

[mu = -(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1), A[0] = 0, A[1] = -RootOf(_Z^2*alpha+gamma*k*w+k^2), B[1] = RootOf(_Z^2*alpha+gamma*k*w+k^2), w = (gamma*k*mu-2*k*sigma)/(gamma*sigma-1)]

 (3)
> 

G1 := U(xi) = 2*RootOf(_Z^2*alpha+gamma*k*w+k^2)/sinh(2*xi)

U(xi) = 2*RootOf(_Z^2*alpha+gamma*k*w+k^2)/sinh(2*xi)

 (4)
> 

pde1 := subs(case1, pde)

I*gamma*(diff(U(xi), xi))*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)+I*gamma*(diff(U(xi), xi))*sigma*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)+gamma*(diff(diff(U(xi), xi), xi))*k*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)-gamma*U(xi)*(4*gamma*k*w+4*k^2-sigma^2)*sigma/(gamma*sigma-1)+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)-U(xi)*sigma^2+U(xi)*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)

 (5)
> 

pde2 := subs(case1, pde1)

I*gamma*(diff(U(xi), xi))*k*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)/(gamma*sigma-1)+I*gamma*(diff(U(xi), xi))*sigma*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)+gamma*(diff(diff(U(xi), xi), xi))*k*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)-gamma*U(xi)*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)*sigma/(gamma*sigma-1)+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)-U(xi)*sigma^2+U(xi)*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)/(gamma*sigma-1)

 (6)
> 

odetest(G1, pde2)
 

NULL

Download test_sol_for_PDE1.mw

How make my plot to have a beter view an...

salim-barzani 1555 Maple 2021
contourplot plotting
September 14 2024
0 1

I don't know how make my graph be beter for real part and imaginary part and abs part which part how work with parameter can any one explain on this example?

G.mw

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