Generation and stabilization of short soliton pulses in the amplified nonlinear Schrödinger equation

Abstract

The nonlinear Schrödinger equation (NLS), with its modified forms, is the central equation for the description of nonlinear pulse propagation in optical fibers. There are a number of different physical situations in which coupling between waves leads to energy transfer. In such systems, ultrashort pulses have been observed to form during propagation. In this paper we show that much of this behavior can be understood by considering the effects of gain in the NLS. We also show that perturbations of the NLS do not destroy these results, provided that the modified equation possesses solitary-wave solutions.