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.
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Keener et al. (1977) studied this question.
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