Collisional Dynamics of Solitons and Pattern Formation in an Integrable Cross Coupled Nonlinear Schrodinger equation with constant background

TL;DR

This paper explores the complex dynamics of solitons in a coupled nonlinear Schrödinger system with a constant background, revealing inelastic collisions, pattern formations, and various localized wave structures through analytical transformations.

Contribution

It introduces a detailed analysis of soliton interactions and pattern formations in an integrable coupled NLSE with constant background, using Gauge and Darboux transformations.

Findings

Inelastic collisional dynamics of bright solitons.

Periodic localization of light pulses facilitated by background field.

Formation of breathers, bright-bright, bright-dark, and dark-bright solitons.

Abstract

We investigate the dynamics arising out of the propagation of light pulses with different polarizations through a condensate (referred to as a constant background field) with cross coupling described by a coupled nonlinear Schrodinger equation(NLSE) type equation. We then employ Gauge and Darboux transformation approach to bring out the rich dynamics arising out of the background field and cross coupling. The collisional dynamics of bright solitons is found to be inelastic. The constant background field is found to facilitate the periodic localization of light pulses during propagation. We have also unearthed breathers, bright-bright, bright-dark and dark-bright solitons of the coupled NLSE. While the amplitude of breathers oscillate with time as predicted, their maximum(or minimum) amplitude is found to remain a constant and the addition of cross coupling only contributes to the rapid fluctuations in its amplitude over a period of time. In addition, the reinforcement of cross coupling in the presence of constant wave field facilitates the interference of light pulses leading to interesting pattern formation among bright-bright, bright-dark and dark-bright solitons. The highlight of the results is that one obtains various localized excitations like breathers, bright and dark solitons by simply manipulating the amplitude of the constant wave field.