Solving Nonlinear Gross Pitaevskii Eq. with Mathematica?

[chasingwind]

I am thinking of solving a nonlinear equation, namely, Gross Pitaevskii equation that applied in Bose Einstein Condensates. Can I solve the equation with Mathematica? Could someone give me some clues?

 

[ReyChiquito]

i think you can get at least a numerical calculation, but here is what we can do, post the equation, ill run it and see what the software can actually do

 

[booth]

I am also interested in solving the Gross-Pitaevskii-Equation. I spend my weekend to get a solution with mathematica without success. There are a couple of Phys. Rev. A.s which treating the problem of numerical solution of the GPE or other non lineary time-(in)dependent Schrödinger-Equations, however it would be much nicer if Mathematica can do such things and I don't have to learn how to write an effective Runge-Kutta.

btw. the time-independent GPE is:

-\hbar^2/(2m) \nabla^2 \psi(x,y,z) + V + g|\Psi(x,y,z)|^2 \Psi(x,y,z) = \mu \Psi(x,y,z)

wherby V = m/2(\omega_x^2 x^2 + \omega_y^2 y^2 + \omega_z^2 z^2)

An other question coming up when I tried getting a solution is: Is it possible to use NDSolve with an other function name than y[x], for example :Psi:[x]? Is it theoretically possible to solve more dimensional (i.e. 3, f[x,y,z]) diff. eq. with NDSolve, which is needed to solve the GPE seriously?

 

[vase]

hi i f u get any way for writting this equation on mathmatica 5 please help me i will appreciate please help me i have to do this for my thesies please help me if u get any sucsses to solve thank u vase moeini from iran

I am also interested in solving the Gross-Pitaevskii-Equation. I spend my weekend to get a solution with mathematica without success. There are a couple of Phys. Rev. A.s which treating the problem of numerical solution of the GPE or other non lineary time-(in)dependent Schrödinger-Equations, however it would be much nicer if Mathematica can do such things and I don't have to learn how to write an effective Runge-Kutta.

btw. the time-independent GPE is:

-\hbar^2/(2m) \nabla^2 \psi(x,y,z) + V + g|\Psi(x,y,z)|^2 \Psi(x,y,z) = \mu \Psi(x,y,z)

wherby V = m/2(\omega_x^2 x^2 + \omega_y^2 y^2 + \omega_z^2 z^2)

An other question coming up when I tried getting a solution is: Is it possible to use NDSolve with an other function name than y[x], for example :Psi:[x]? Is it theoretically possible to solve more dimensional (i.e. 3, f[x,y,z]) diff. eq. with NDSolve, which is needed to solve the GPE seriously?