Optical soliton propagation in a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equations

Abstract

Optical soliton propagation in fibres with resonant impurities and erbium-doped nonlinear systems are considered. The fibre system is governed by the coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equations. The system equations using Painlevé analysis are found to be completely integrable, but only when the parameters involving the group velocity dispersion, Kerr nonlinearity and the field interaction with the atoms, satisfy a particular condition. With a suitable approximation, for the first time Painlevé analysis of the system equation is reported in this paper. The Lax pair of the system equation is explicitly constructed. The single soliton solution is also explicitly derived using the Darboux-Bäcklund transformation method.