Dynamics of nondegenerate solitons in long-wave short-wave resonance interaction system

TL;DR

This paper investigates the dynamics of nondegenerate vector solitons in a long wave-short wave resonance interaction system, revealing novel collision behaviors and physical implications across various nonlinear physical contexts.

Contribution

It introduces a new class of nondegenerate vector soliton solutions with distinct velocities, analyzed via Hirota's method, and explores their collision dynamics and physical relevance.

Findings

Identification of nondegenerate vector solitons with distinct velocities.

Discovery of three types of elastic collision scenarios, including a novel shape-changing collision.

Potential applications in nonlinear optics, hydrodynamics, and Bose-Einstein condensates.

Abstract

In this paper, we study the dynamics of an interesting class of vector solitons in the long wave-short wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of the long-wave and two-short waves and it generically appears in several physical settings. To derive this class of nondegenerate vector soliton solutions we adopt the Hirota bilinear method with the more general form of admissible seed solutions with nonidentical distinct propagation constants. We express the resultant fundamental as well as multi-soliton solutions in a compact way using Gram-determinants. The general fundamental vector soliton solution possesses several interesting properties. For instance, the double-hump or a single-hump profile structure including a special flattop profile form results in when the soliton propagates in all the components with identical velocities. Interestingly, in the case of nonidentical velocities, the soliton number is increased to two in the long-wave (LW) component, while a single-humped soliton propagates in the two short-wave (SW) components. We establish through a detailed analysis that the nondegenerate multi-solitons in contrast to the already known vector solitons (with identical wave numbers) can undergo three types of elastic collision scenarios: (i) shape preserving, (ii) shape altering, and (iii) a novel shape changing collision, depending on the choice of the soliton parameters. In addition, we point out the coexistence of nondegenerate and degenerate solitons simultaneously along with the associated physical consequences. We also indicate the physical realizations of these general vector solitons in nonlinear optics, hydrodynamics, and Bose-Einstein condensates. Our results are generic and they will be useful in these physical systems and other closely related systems including plasma physics.