Optical solitons in an erbium-doped nonlinear fibre medium with higher order dispersion and self-steepening

Abstract

A coupled system of the Hirota equation and the Maxwell-Bloch (H-MB) equations which explains wave propagation in an erbium-doped nonlinear fibre with higher order dispersion and self-steepening is proposed. The integrability aspects of the H-MB equations are analysed through Painlevé analysis. The Lax pair is explicitly constructed, and the soliton solution is obtained from it using Darboux-Bäcklund transformations. Thus the proposed coupled system of H-MB equations is found to admit soliton type lossless propagation.