NONLINEAR SCHRODINGER-EQUATION AND N-SOLITON INTERACTIONS - GENERALIZED KARPMAN-SOLOVEV APPROACH AND THE COMPLEX TODA CHAIN

method for the description of the N-soliton interaction, which general izes in a natural way the Karpman-Solov'ev one for the nonlinear Schro dinger (NLS) equation, is proposed. Using it, we derive a nonlinear sy stem of equations describing the dynamics of the parameters of N well separated solitons with nearly equal amplitudes and velocities. Next w e study an exhaustive list of perturbations, relevant for nonlinear op tics, which include linear and nonlinear dispersive and dissipative te rms, effects of sliding filters, amplitude and phase modulation, etc. We prove that the linear perturbations affect each of the solitons sep arately, while the nonlinear ones also lead to additional interactive terms between neighboring solitons. Under certain approximations we sh ow that the N-soliton interaction for the unperturbed NLS equation is described by the complex Toda chain (CTC) with N nodes, which is a com pletely integrable dynamical system with 2N degrees of freedom. A comp arison made by numeric simulation shows that CTC gives an adequate des cription for the soliton interactions for a number of choices of the i nitial conditions.