  Using the Karpman-Solov'ev method we derive the equations for the 2-soliton
adiabatic interaction for solitons of the modified nonlinear Schrodinger
equation (MNSE). Then we generalize these equations to the case of N
interacting solitons with almost equal velocities and widths. On the basis of
this result we prove that the N MNSE-soliton train interaction (N>2) can be
modeled by the completely integrable complex Toda chain (CTC). This is an
argument in favor of universality of the complex Toda chain which was
previously shown to model the soliton train interaction for nonlinear
Schrodinger solitons. The integrability of the CTC is used to describe all
possible dynamical regimes of the N-soliton trains which include asymptotically
free propagation of all N solitons, N-soliton bound states, various mixed
regimes, etc. It allows also to describe analytically the manifolds in the
4N-dimensional space of initial soliton parameters which are responsible for
each of the regimes mentioned above. We compare the results of the CTC model
with the numerical solutions of the MNSE for 2 and 3-soliton interactions and
find a very good agreement.
