Adiabatic Interactions of Manakov Solitons -- Effects of Cross-modulation

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.