Solitons in Ideal Optical Fibers - A Numerical Development

TL;DR

This paper introduces a numerical method combining finite difference and relaxation Gauss-Seidel techniques to simulate soliton propagation in ideal optical fibers, validated against known analytical solutions.

Contribution

It presents a new numerical procedure for solving PDEs related to soliton propagation in optical fibers, demonstrating its accuracy and effectiveness.

Findings

The numerical method accurately replicates analytical soliton solutions.

The procedure effectively models soliton wave propagation in ideal optical fibers.

Validation confirms the method's suitability for simulating optical solitons.

Abstract

This work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers.