A comparison between the Split Step Fourier and Finite-Difference method in analysing the soliton collision of a type of Nonlinear Schr\"odinger equation found in the context of optical pulses

TL;DR

This paper compares the Split Step Fourier and Finite Difference methods for analyzing soliton collisions in a nonlinear Schrödinger equation relevant to optical pulses, highlighting the advantages of the Split Step approach.

Contribution

It provides a comparative analysis of two numerical schemes for solving a specific nonlinear Schrödinger equation in optical pulse research, demonstrating the superiority of the Split Step Fourier method.

Findings

Split Step Fourier method outperforms Finite Difference in this context

The dynamics depend significantly on parameter S values

Numerical schemes reveal different behaviors in soliton collision analysis

Abstract

In this report a type of Schr\"odinger Equation which is found in the context of optical pulses is analysed using the $\textit{Split Step}$ and $\textit{Finite Difference}$ method. The investigation shows interesting dynamics regarding certain values for parameter $S$ as well as a comparison between the two numeric schemes demonstrating the $\textit{Split Step}$ to be superior for this problem.