Multicomponent long-wave--short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons

TL;DR

This paper analyzes a multicomponent (2+1)-dimensional long-wave--short-wave resonance system, deriving exact soliton solutions, studying their interactions, and exploring resonant and rogue wave formations.

Contribution

It presents the integrability, exact multi-soliton solutions, and detailed collision dynamics of a novel multicomponent LSRI system with arbitrary nonlinearities.

Findings

Demonstrated integrability via Painlevé analysis.

Constructed explicit bright and dark soliton solutions.

Identified energy-sharing and resonant soliton phenomena.

Abstract

We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long-wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlev\'e analysis. Then we construct the exact bright multi-soliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.