  We analyze the dynamical behavior of the N-soliton train in the adiabatic
approximation of the perturbed nonlinear Schrodinger (NLS) equation and the
Manakov model. The perturbations include the simultaneous by a periodic
external potential, and linear and nonlinear gain/loss terms. We derive the
corresponding perturbed complex Toda chain (PCTC) models for both NLS and
Manakov model. We show that the soliton interactions dynamics for the PCTC
models compares favorably to full numerical results of the original perturbed
NLS and Manakov model.
