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Transformation of strange equation In PDE to ODE h...

Asked by: salim-barzani 185
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

Can you find what values in a procedure are giving...

Asked by: Hullzie16 328
ode rootfinding dsolve
October 11 2024
1  10

I have a procedure that I am trying to run that would be an improvement/more sophisticated way of solving a problem that I have previously solved. When I try and run my procedure I am getting an error, and from what I gather with the error is that there are some values when inserted into my procedure that cannot be evaluated. Just for context it is a procedure that contains numerical solutions to a system of DEs and and contains inequalities. 

I would like to know is there an easy method to figure out what values are giving me this error? 

Or a follow up, is there something wrong with my procedure that is giving me this error? I have included some commentary in my workshet as well to hopefully make everything clear. 

Thanks. 

Proc_Error.mw

boundaries of integral...

Asked by: charlie_fcl 130
integration pi
October 11 2024
0  0

Hi,

I just got 2 questions regarding symbols and answers in MapleFlow (I might be doing something wrong here).

- In trying to input the integral int(F(x), x = -pi/5 .. pi/5) - this is just an example! - as a symbol,

int(F(x), x = -pi/5 .. pi/5)

MapleFlow doesn´t accept fractions or multiplications for bondaries values, unless I input "int(F(x), x = -pi/5 .. pi/5 =". Is there anyway to do it?

- is it possible to have the answer as 2*cos((3*Pi)/10), like in Maple, instead of 2.00*cos(300e-3*pi) ()symbolic expression) or 1.18 (numeric expression)?

Thanks in advance for your help.

How to read a *.m file written many years ago?...

Asked by: Michael 232
read printf dotm
October 11 2024
1