On the Stability of Soliton-Like Pulses in a Nonlinear Dispersive System with Instability and Dissipation

Abstract

The stability of various equilibrium solutions of a strongly dispersive nonlinear system with instability and dissipation is investigated both numerically and analytically. Periodic trains of soliton-like pulses are found to be stable when the distance between adjacent pulses becomes smaller than a critical value. This critical value is determined by linear stability analysis. A modulational type instability is also observed for a very long string of soliton-like pulses even when the fundamental distance is within the stable regime.