Higher dimensional bright solitons and their collisions in multicomponent long wave-short wave system

TL;DR

This paper derives bright soliton solutions for a (2+1)-dimensional multicomponent wave system, revealing unique collision behaviors and amplification effects, with potential applications in nonlinear wave dynamics.

Contribution

It introduces the first (to our knowledge) study of shape-changing collisions of multicomponent solitons in (2+1) dimensions and generalizes solutions to an ($n+1$)-wave system.

Findings

Short wave solitons can be amplified by reducing long wave pulse width.

Short wave solitons undergo shape-changing collisions with intensity redistribution.

Long wave solitons exhibit elastic collisions with phase shifts.

Abstract

Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one long wave component are found and then the results are generalized to the corresponding integrable ($n+1$)-wave system with $n$ short waves and single long wave. It is shown that the solitons in the short wave components (say $S^{(1)}$ and $S^{(2)}$) can be amplified by merely reducing the pulse width of the long wave component (say L). The study on the collision dynamics reveals the interesting behaviour that the solitons which split up in the short wave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though similar type of collision is possible in (1+1) dimensional multicomponent integrable systems, to our knowledge for the first time we report this kind of collisions in (2+1) dimensions. However, solitons which appear in the long wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.