Numerical Investigation of Spatial Solitons

Abstract

The numerical method we have previously developed to search for soliton solutions is applied in this article to find spatial solitons described by a nonlinear Schroedinger equation. We show in detail how to derive the Schroedinger equation from Maxwell’s equations and now to construct a one-soliton analytical solution for the one-dimensional Schroedinger equation. The proposed numerical method is appropriate to search for spatial solitons, which is corroborate by comparing the numerical results with the analytical solution.