N-soliton train interactions and perturbed complex Toda chain in nonlinear optics. Adiabatic and non-adiabtic aspects

摘要

Our previous results on the N-soliton interaction in the adiabaticapproximation have been extended. It is shown that the complex Toda chain (CTC)model is an universal one in the sense that it describes the N-soliton traininteractions for all NLEE from the NLS hierarchy. We derive the perturbed CTCsystem and show that the small perturbations affect only the center of massmotion and the global phase of the N-soliton train. A special reduction of CTCknown as the Toda chain with indefinite metric describes the interaction of thesine-Gordon solitons and anti-solitons. The peculiarities of the interactionsin the non-adiabatic cases are outlined.