Different types of nonlinear localized and periodic waves in an erbium-doped fiber system

TL;DR

This paper explores the diverse nonlinear localized and periodic wave solutions in an erbium-doped fiber system, revealing multiple wave types and their explicit conditions through a unified exact solution.

Contribution

It provides a comprehensive analysis of various nonlinear wave types in an erbium-doped fiber system using a unified exact solution approach.

Findings

Existence of multi-peak soliton, periodic wave, antidark soliton, and W-shaped soliton.

Explicit conditions for the existence of these nonlinear waves.

Demonstration of the structural diversity of nonlinear waves in the system.

Abstract

We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schr\"odinger and the Maxwell-Bloch equations. We find that prolific different types of nonlinear localized and periodic waves do exist in the system, including multi-peak soliton, periodic wave, antidark soliton, and W-shaped soliton (as well as the known bright soliton, breather, and rogue wave). In particular, the dynamics of these waves can be extracted from a unified exact solution, and the corresponding existence conditions are presented explicitly. Our results demonstrate the structural diversity of the nonlinear waves in this system.