Soliton Perturbations: A Variational Principle for the Soliton Parameters

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Abstract
A variational perturbation method is developed to study the evolution of a single soliton in the presence of small perturbations. Adiabatic evolution equations for the parameters of the soliton are derived to first order in the perturbation without employing methods or results from the inverse scattering theory. The analysis accounts for the effects of shape modifications in the form of a "dress" or "tail" of the soliton. The method is applied to the perturbed Korteweg-deVries, modified Korteweg-deVries, nonlinear Schrödinger and sine-Gordon equations and the results are compared with those obtained from other approaches.