Numerically solving NLS equation

hanson

Hi all.
I am using the Split Step Fourier Method to solve NLS to study the interaction of two solitons.
I have done the animation of the collision of two solitons for exact solution.

But when I numerically solve it and watch the animation, the profiles during interaction is not quite the same. I don't really know what's wrong. I have used a finer step size to try again. But it doesn't help.

Will the numerical solution resemble the exact solution very well during interaction?

Can you kindly refer me to some animations of NLS soliton collision using numerical solutions? I am using the NLS in water wave context in the most simple form, namely iut+uxx+u^2u=0.

jdg812

It gonna be
iut + uxx + |u|^2u = 0