  We investigate the asymptotic behavior of the Manakov soliton trains
perturbed by cross-modulation in the adiabatic approximation. The multisoliton
interactions in the adiabatic approximation are modeled by a generalized
Complex Toda chain (GCTC). The cross-modulation requires special treating for
the evolution of the polarization vectors of the solitons. The numerical
predictions of the Manakov system are compared with the perturbed GCTC. For
certain set of initial parameters GCTC describes very well the long-time
evolution of the Manakov soliton trains.
