Bright, dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

TL;DR

This paper derives and analyzes bright, dark, and breather soliton solutions for a generalized long-wave short-wave resonance system, revealing their behaviors, interactions, and special states in nonlinear wave dynamics.

Contribution

It introduces explicit N-soliton solutions in Gram determinant form for the system, including novel resonance interactions and bound states not previously characterized.

Findings

Fundamental bright solitons can behave like KdV or NLS solitons.

Dark solitons exhibit anti-dark, grey, and black profiles.

Solitons undergo elastic collisions with phase shifts.

Abstract

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the Hirota bilinear method, the general $N$-bright and $N$-dark soliton solutions are deduced and their Gram determinant forms are obtained. A special feature of the fundamental bright soliton solution is that, in general, it behaves like the Korteweg-deVries soliton. However, under a special condition, it also behaves akin to the nonlinear Schr\"{o}dinger soliton when it loses the amplitude dependent velocity property. The fundamental dark-soliton solution admits anti-dark, grey, and completely black soliton profiles, in the short-wave component, depending on the choice of wave parameters. On the other hand, a bright soliton like profile always occurs in the long-wave component. The asymptotic analysis shows that both the bright and dark solitons undergo an elastic collision with a finite phase shift. In addition to these, by tuning the phase shift regime, we point out the existence of resonance interactions among the bright solitons. Furthermore, under a special velocity resonance condition, we bring out the various types of bright and dark soliton bound states. Also, by fixing the phase factor and the system parameter $\beta$, corresponding to the interaction between long and short wave components, the different types of profiles associated with the obtained breather solution are demonstrated.