# Urgent - important question regarding SSFM

1. Jun 2, 2010

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 doesnt matter ?

furthermore, you think it is possible to solve itusing the matlab solver for PDE ?
John.

Last edited: Jun 2, 2010
2. Jun 2, 2010

### 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.

3. Jun 2, 2010

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 ?

4. Jun 3, 2010

### 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.