Adiabatic and non-adiabatic soliton interactions in nonlinear optics

Our previous results on the N-soliton interaction in the adiabatic approximation have been 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. A special reduction of CTC describes the interaction of the sine-Gordon solitons and anti-solitons. The peculiarities of the interactions in the non-adiabatic cases are outlined.