Exact Solutions for Wave Propagation in Birefringent Optical Fibers

TL;DR

This paper uses group theory to find exact solutions, including solitons, for coupled nonlinear Schrödinger equations modeling wave propagation in birefringent optical fibers.

Contribution

It introduces a symmetry-based method to derive explicit solutions for the nonlinear equations governing birefringent fiber optics.

Findings

Derived explicit soliton solutions

Identified symmetry algebra of the equations

Provided examples of exact wave profiles

Abstract

We carry out a group-theoretical study of the pair of nonlinear Schr\"{o}dinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to provide examples of specific exact solutions. Among them, we obtain the soliton profile, which is related to the coordinate translations and the constant change of phase.