A numerical development in the dynamical equations of solitons into ideal optical fibers

TL;DR

This paper presents a numerical method using finite element techniques to accurately simulate soliton propagation in ideal optical fibers, aligning well with known analytical solutions.

Contribution

It introduces a stabilized finite element approach for solving nonlinear differential equations governing solitons in optical fibers, enhancing numerical accuracy and stability.

Findings

Numerical solutions match analytical results closely.

Stabilization methods improve solution accuracy.

Finite element method effectively models soliton dynamics.

Abstract

We develop and evaluate a numerical procedure for a system of nonlinear differential equations, which describe the propagation of solitons into ideal dielectric optical fibers. This problem has analytical solutions known. The numerical solutions of the system is implemented by the finite element method, using methods of stabilization such as Streamline Upwind Petrov-Galerkin (SUPG) and Consistent Approximate Upwind (CAU). Comparing the numerical and analytical solutions, it was found that the numerical procedure adequately describes the dynamics of this system.