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Using the Karpman-Solov'ev method we derive the equations for the 2-solitonadiabatic interaction for solitons of the modified nonlinear Schrodingerequation (MNSE). Then we generalize these equations to the case of Ninteracting solitons with almost equal velocities and widths. On the basis ofthis result we prove that the N MNSE-soliton train interaction (N>2) can bemodeled by the completely integrable complex Toda chain (CTC). This is anargument in favor of universality of the complex Toda chain which waspreviously shown to model the soliton train interaction for nonlinearSchrodinger solitons. The integrability of the CTC is used to describe allpossible dynamical regimes of the N-soliton trains which include asymptoticallyfree propagation of all N solitons, N-soliton bound states, various mixedregimes, etc. It allows also to describe analytically the manifolds in the4N-dimensional space of initial soliton parameters which are responsible foreach of the regimes mentioned above. We compare the results of the CTC modelwith the numerical solutions of the MNSE for 2 and 3-soliton interactions andfind a very good agreement.Comment: 28 pages, 6 figures, LaTeX 2e article styl

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Adiabatic interaction of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>ultrashort solitons: Universality of the complex Toda chain model

Adiabatic interaction ofNultrashort solitons: Universality of the complex Toda chain model