Perturbation of parametrically excited solitary waves

A direct perturbation analysis of solitary waves for a parametric Ginzburg Landau equation describing parametric excitation of waves in nonlinear dispersive and dissipative systems is presented. The method is used to study the influence on soliton dynamics of various perturbations, including external fields, stochastic driving forces, higher-order effects, and soliton interactions. A remarkable and quite general result of the analysis is that when the system is dissipative the dynamical motion induced by the perturbation is counteracted by the dissipative term, making dissipative solitary waves less sensitive to perturbations than solitons in the conservative case. copyright 1997 The American Physical Society