Evolution theorem for a class of perturbed envelope soliton solutions

Abstract

Envelope soliton solutions of a class of generalized nonlinear Schrödinger equations are investigated. If the quasiparticle number N is conserved, the evolution of solitons in the presence of perturbations can be discussed in terms of the functional behavior of N(η2), where η2 is the nonlinear frequency shift. For ∂η2N >0, the system is stable in the sense of Liapunov, whereas, in the opposite region, instability occurs. The theorem is applied to various types of envelope solitons such as spikons, relatons, and others.