Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation

A comprehensive analysis is presented of the propagation of symmetry-endowed two-soliton solutions under the influence of various perturbations important in nonlinear optics. Thus, we begin by introducing the analytical expressions of these two-soliton solutions. Then, by considering perturbations which preserve the initial symmetry of the two-soliton solutions, the dependence of the soliton parameters on the propagation distance is determined by using an adiabatic perturbation method. As perturbations of this kind, important for soliton-based communication systems, we consider the bandwidth-limited amplification, nonlinear amplification, and amplitude and phase modulation. Moreover, the results obtained by the adiabatic perturbation method are compared with those obtained by direct numerical simulations of the corresponding governing differential equations.