Manakov model with gain/loss terms and $N$-soliton interactions: Effects of periodic potentials

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.