Rogue waves in a resonant erbium-doped fiber system with higher-order effects

TL;DR

This paper investigates rogue wave solutions in a complex erbium-doped fiber system with higher-order effects, deriving explicit solutions using Darboux transformations and exploring their properties.

Contribution

It introduces a novel method for constructing rogue wave solutions in a coupled nonlinear Schrödinger-Maxwell-Bloch system with higher-order effects.

Findings

Derived Darboux transformation for the system.

Constructed explicit rogue wave solutions.

Explored hybrid rogue wave and breather solutions.

Abstract

We mainly investigate a coupled system of the generalized nonlinear Schr\"odinger equation and the Maxwell-Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the forth-order dispersion and quintic non-Kerr nonlinearity. We derive the one-fold Darbox transformation of this system and construct the determinant representation of the $n$-fold Darboux transformation. Then the determinant representation of the $n$th new solutions $(E^{[n]},\, p^{[n]},\, \eta^{[n]})$ which were generated from the known seed solutions $(E, \, p, \, \eta)$ is established through the $n$-fold Darboux transformation. The solutions $(E^{[n]},\, p^{[n]},\, \eta^{[n]})$ provide the bright and dark breather solutions of this system. Furthermore, we construct the determinant representation of the $n$th-order bright and dark rogue waves by Taylor expansions and also discuss the hybrid solutions which are the nonlinear superposition of the rogue wave and breather solutions.