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

TL;DR

This paper investigates how periodic potentials and gain/loss terms influence N-soliton interactions in the Manakov model, using a perturbed complex Toda chain approach validated by numerical simulations.

Contribution

It introduces a perturbed complex Toda chain model for the Manakov system with gain/loss and periodic potentials, extending previous models and providing accurate predictions.

Findings

PCTC models match numerical simulations well.

Periodic potentials significantly affect soliton dynamics.

Gain/loss terms modify interaction behaviors.

Abstract

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.