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We investigate the asymptotic behavior of the Manakov soliton trainsperturbed by cross-modulation in the adiabatic approximation. The multisolitoninteractions in the adiabatic approximation are modeled by a generalizedComplex Toda chain (GCTC). The cross-modulation requires special treating forthe evolution of the polarization vectors of the solitons. The numericalpredictions of the Manakov system are compared with the perturbed GCTC. Forcertain set of initial parameters GCTC describes very well the long-timeevolution of the Manakov soliton trains.

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