Solving an Equation with the SSFM Method - John's Urgent Question

[Johnbasko]

hello all
Im trying to solve the equation:

i*dV/dt = d^2V/dz^2 + V*sqrt(1-V^2)

I want to try by the split step Fourier method.

My problem is that most of the code/solvers I saw that implement the SSFM method are when the evolution is in space not in time, meaning the first derivative is d/dz and the second is (d/dt)^2

any idea how it fact or maybe it doesn't matter ?

furthermore, you think it is possible to solve itusing the MATLAB solver for PDE ?
thanks in advance
John.

 

[Mute]

In your equation, replace z with t and t with z:

i*dV/dz = d^2V/dt^2 + V*sqrt(1-V^2)

Is this the form you require to use the split-step method? If so, all I've done is a cosmetic change; time is now labeled by z and space is now labeled by t. So, it looks like the method should work with your equation based on what you've said.

 

[Johnbasko]

Mute, thank you for the response.

Ofcourse, I understand this cosmetic changed, and indeed, by this change the form is regular.
But, I wonder if it's is allow, I mean if this changed might influence on the result of the SSFM method i will use in this equation ?
or the result should be okay ?

In all the material I've looked I've noticed that always the evolution (i.e: the first derivative) if on the space (Z domain), so infact my question whether this cosmetic change might harm the result or all should be the same ?
Thanks

p.s: Furthermore, I would like to know if anyone know an organized source code for the SSFM ?

 

[Mute]

It shouldn't make any difference. The label t for time or z for space is just a convenience to us; the computer doesn't know that 'z' is space or 't' is time. You're the one who decides how to interpret the labels, so you can freely interpret z as time. So, if you make that cosmetic change and run the program, all you have to do is interpret the output properly, remembering that after the cosmetic change time is now z and space is now t.