Coexistence of a self-induced transparency soliton and a higher order nonlinear Schrödinger soliton in an erbium doped fiber

We consider the wave propagation in an erbium doped nonlinear fiber media. The wave equation which governs the system forms three groups. The first one is the well known coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch (NLS-MB) equations. Including the higher order effects like the higher order dispersion, self steepening and the stimulated inelastic scattering we propose the other two systems. The systems are the coupled system of the Hirota equation and the Maxwell-Bloch (H-MB) equations and the higher order nonlinear Schrödinger equation and the Maxwell-Bloch (HNLS-MB) equations. All the three systems allow soliton type pulse propagation only under certain parametric conditions between the physical parameters involved in the system. The Lax pairs of the system equations are explicitly shown. The single soliton solutions are constructed using the Bäcklund transformation