Thread Subject: Solving Time and Space dependent set of equations

Hi, I'd like to solve a set of 3 nonlinear, space and time dependent complex equations but don't know how to implement it with ODE solver.

My 3 equations :

i*hbar*dpsi1(x,y,t)/dt=A*Laplacian(psi1(x,y,t))
+B*(|psi1(x,y,t)|^2+|psi2(x,y,t)|^2+|psi3(x,y,t)|^2)

i*dpsi2(x,y,t)/dt=A*Laplacian(psi2(x,y,t))
+B*(|psi1(x,y,t)|^2+|psi2(x,y,t)|^2+|psi3(x,y,t)|^2)

i*dpsi3(x,y,t)/dt=A*Laplacian(psi3(x,y,t))
+B*(|psi1(x,y,t)|^2+|psi2(x,y,t)|^2+|psi3(x,y,t)|^2)

with respect to psi1, psi2 & psi3

A and B some constants and | | stands for the norm.

Your ideas are welcome, Thanks by advance...

"Hugo " <polal2is@neuf.fr> wrote in message <hejh8p$p3r$1@fred.mathworks.com>...
> Hi, I'd like to solve a set of 3 nonlinear, space and time dependent complex equations but don't know how to implement it with ODE solver.
>
> My 3 equations :
>
> i*hbar*dpsi1(x,y,t)/dt=A*Laplacian(psi1(x,y,t))
> +B*(|psi1(x,y,t)|^2+|psi2(x,y,t)|^2+|psi3(x,y,t)|^2)
>
> i*dpsi2(x,y,t)/dt=A*Laplacian(psi2(x,y,t))
> +B*(|psi1(x,y,t)|^2+|psi2(x,y,t)|^2+|psi3(x,y,t)|^2)
>
> i*dpsi3(x,y,t)/dt=A*Laplacian(psi3(x,y,t))
> +B*(|psi1(x,y,t)|^2+|psi2(x,y,t)|^2+|psi3(x,y,t)|^2)
>
> with respect to psi1, psi2 & psi3
>
> A and B some constants and | | stands for the norm.
>
> Your ideas are welcome, Thanks by advance...

1) Are you sure you don't need an hbar factor on the 2nd and 3rd as well ?
2) These are PDEs, you cant' use an ODE solver on them straight away.
3) To apply any numerical method to those you have 1st to specify the problem: initial or boundary value ? What initial or boundary conditions are applied ?

You're right I forgot some hbar, what about using the PDE toolbox instead ?

"Hugo " <polal2is@neuf.fr> wrote in message <hejljr$3nl$1@fred.mathworks.com>...
> You're right I forgot some hbar, what about using the PDE toolbox instead ?

Never used it, I'm afraid, but I doubt it can be applied directly to your equations. You'll have to formulate your problem better anyway. Remember your PSIs are generally complex-valued functions and until you define A, B, the domain and the initial/boundary value conditions you don't even know how many dimensions you have to numerically integrate on.
How about some Monte-Carlo calcs ?

"Riccardo" <nothx@nospam.org> wrote in message <hejn4j$932$1@fred.mathworks.com>...
> "Hugo " <polal2is@neuf.fr> wrote in message <hejljr$3nl$1@fred.mathworks.com>...
> > You're right I forgot some hbar, what about using the PDE toolbox instead ?
>
> Never used it, I'm afraid, but I doubt it can be applied directly to your equations. You'll have to formulate your problem better anyway. Remember your PSIs are generally complex-valued functions and until you define A, B, the domain and the initial/boundary value conditions you don't even know how many dimensions you have to numerically integrate on.
> How about some Monte-Carlo calcs ?

Of course my psi are complex and I will have to transform my 2x2 matrix to vectors and also separate Imaginary parts from real parts, and this way I'll be able to do something with ODE I think (tough to do though). Monte Carlo is an Idea and is often used to solve these gross pitaevskii equations, I'll have a look...