Multi-soliton propagation in a generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with loss/gain driven by an external potential

In this paper, we introduce a system of the nonlinear Schrödinger-Maxwell-Bloch equation with variable coefficients which represents the propagation of optical pulses in an inhomogeneous erbium doped fiber with loss/gain driven by an external potential. The one and two soliton solutions in explicit forms are generated by using the Darboux transformation and the associated Lax pair. We consider the distributed amplification system, and some main features of the solutions are demonstrated graphically. We also consider the concept of soliton propagation in a dispersion managed erbium doped fiber and through symbolic computation, we have carried out our study from an analytic viewpoint.