Dynamics of the Ablowitz-Ladik soliton train

It is shown that dynamics of a train of N weakly interacting Ablowitz-Ladik solitons with (almost) equal velocities and masses is governed by the complex Toda chain model. The integrability of the complex Toda chain model provides the means to describe analytically various dynamical regimes of the N-soliton train and to predict initial soliton parameters responsible for each of the regimes. Numerical simulations corroborate well analytical predictions. A specific feature arising for the discrete soliton train system is the appearance of an additional (with respect to the lattice spacing) spatial scale-intersoliton distance. We comment on interplay between both spatial scales.