Asymptotic Behavior of Manakov Solitons: Effects of Potential Wells and Humps

TL;DR

This paper investigates how external potential wells and humps influence the long-term behavior of Manakov solitons, demonstrating that a perturbed integrable model accurately predicts their asymptotic dynamics.

Contribution

It extends the complex Toda chain model to include external potentials and validates its effectiveness in predicting Manakov soliton behavior under such perturbations.

Findings

Perturbed CTC reliably predicts long-time soliton evolution.

External potentials significantly affect soliton interactions.

Numerical results match theoretical predictions across regimes.

Abstract

We consider the asymptotic behavior of the soliton solutions of Manakov's system perturbed by external potentials. It has already been established that its multisoliton interactions in the adiabatic approximation can be modeled by the Complex Toda chain (CTC). The fact that the CTC is a completely integrable system, enables us to determine the asymptotic behavior of the multisoliton trains. In the present study we accent on the 3-soliton initial configurations perturbed by sech-like external potentials and compare the numerical predictions of the Manakov system and the perturbed CTC in different regimes. The results of conducted analysis show that the perturbed CTC can reliably predict the long-time evolution of the Manakov system.