Perturbed Complex Toda Chain and Soliton Interactions in Nonlinear Optics

Abstract

Our previous results on the $N$-soliton interaction in the adiabatic approximation are extended. It is shown that the complex Toda chain (CTC) model is a universal one in the sense that it describes the $N$-soliton train interactions for all NLEE from the NLS hierarchy. We derive the perturbed CTC system and show that the small perturbations affect only the center of mass motion and the global phase of the $N$-soliton train. The peculiarities of the interactions in the nonadiabatic cases are outlined.