General two-component long-wave short-wave resonance interaction system: Non-degenerate vector solitons and their collision dynamics

TL;DR

This paper introduces a new integrable two-component long-wave-short-wave resonance interaction model that features non-degenerate solitons with novel profiles and collision behaviors, analyzed through Hirota's method.

Contribution

It provides the first explicit N-soliton solutions for this model, classifies non-degenerate solitons, and studies their collision dynamics and profile structures.

Findings

Non-degenerate solitons exhibit double-hump, flat-top, and single-hump profiles.

Soliton collisions can be shape-preserving or shape-changing, with some becoming elastic after shifts.

The model's results are applicable to Bose-Einstein condensates, nonlinear optics, and plasma physics.

Abstract

In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave-short-wave resonance interaction model with a general form of nonlinearity coefficients. Through the classical Hirota's bilinear method, we obtain a fully non-degenerate $N$-soliton solution in Gram determinant form for this LSRI model. Depending on the choice of velocity conditions, the obtained non-degenerate fundamental soliton is classified into two types, namely ($1,1,1$)- and ($1,1,2$)-non-degenerate one solitons. We then show that the basic ($1,1,1$)-non-degenerate soliton exhibits novel profile structures, including a double-hump, a special flat-top, and a conventional single-hump profile, and ($1,1,2$)-non-degenerate soliton admits two-soliton like oblique collision, a behavior akin to KP line soliton interaction with a short stem structure. A detailed asymptotic analysis is carried out to study the long time behavior of ($1,1,1$)-non-degenerate solitons and it reveals that they undergo both shape-preserving and shape-changing collisions. However, our analysis confirms that the shape changing collision between these solitons become elastic in nature after appropriate shift of time coordinates. Further, we identified that the ($1,1,2$)-non-degenerate solitons also undergo elastic collision. In addition, we have also investigated the formation or suppression of breathing phenomena during collision between a degenerate soliton and a ($1,1,1$)-non-degenerate soliton. For completeness, we also point out the collision scenario between the completely degenerate solitons. The results presented in this paper are broadly applicable to Bose-Einstein condensates, nonlinear optics, plasma physics, and other closely related fields.