Solitons under perturbations

Abstract

A direct perturbation method is developed in order to study the interactions of $N$ solitons with imperfections and with each other in the presence of imperfections. The leading-order effects are obtained directly from the $N$-soliton waveform without invoking methods from inverse-scattering theory. The method is based upon a Green's function and a "two time" procedure from classical perturbation theory. An example of a single soliton is developed in detail. Finally, this perturbation method is compared with other approaches in the literature.