I am solving the NLSE (nonlinear schroedinger equation) using the Fourier Split Step Method in MATLAB. To avoid MATLAB's boundary reflection problems and phase discontinuity's you naturally have to make the time/freq windows very very large. As a consequence you need to considerably increase the number of points and hence simulation time...Except increasing the number of points also makes your pulse less visible.

My question is whether or not their is a way to either:

- avoid the fourier transform boundary reflections OR

- some how create a code that takes more points where your actual 'pulse of light' is and less points in the region where nothing exists.