Soliton solutions to the coupled Sasa-Satsuma-mKdV equation

TL;DR

This paper investigates various soliton solutions of a coupled Sasa-Satsuma-mKdV equation, analyzing their properties, interactions, and collision behaviors under different boundary conditions.

Contribution

It introduces a comprehensive classification of soliton solutions for the coupled equation and analyzes their collision dynamics, including inelastic and kink interactions.

Findings

Four classes of soliton solutions identified: bright-bright, dark-dark, bright-dark, dark-bright.

Inelastic collisions observed between bright-bright solitons.

Unique soliton profiles and interactions, including kink-soliton collisions, are characterized.

Abstract

We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-mKdV equation using the Kadomtsev-Petviashvili reduction method. The system consists of a complex-valued component coupled with a real-valued one. Under zero or nonzero boundary conditions, we derive four distinct classes of soliton solutions: bright-bright, dark-dark, bright-dark, and dark-bright. These solutions are derived from the vector Hirota equation, for which the bright, dark, and bright-dark soliton solutions are provided in the Appendix. We perform asymptotic analysis of soliton collisions for each class of solutions, in which inelastic collisions are observed between bright-bright solitons. In the dark-dark case, we identify soliton profiles similar to the Sasa-Satsuma equation, including double-hole, Mexican hat, and anti-Mexican hat solutions; this study further explores the collisions between these structures and hyperbolic tangent shaped kink solitons. Regarding the bright-dark case, beyond the expected soliton-kink interactions, we report and analyze a notable collision occurring between kink solitons.