Multiple soliton solutions and similarity reduction of a (2+1)-dimensional variable-coefficient Korteweg-de Vries system

TL;DR

This paper derives multiple soliton solutions and similarity reductions for a (2+1)-dimensional variable-coefficient KdV system, revealing complex wave interactions and physical features through analytic methods.

Contribution

It introduces novel analytic solutions, including N-solitons and hybrid lump, breather, and line solitons, for the variable-coefficient (2+1)D KdV system using Hirota's method.

Findings

Derived N-soliton solutions via Hirota's bilinear method

Constructed hybrid solutions combining lump, breather, and line solitons

Analyzed similarity solutions and Painlevé equations revealing physical wave features

Abstract

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in particular, the hybrid solution of lump, breather and line soliton are derived by the long wave limit method. In addition to soliton solutions, similarity reduction, including similarity solutions (also known as group-invariant solutions) and non-autonomous third-order Painlev\'e equations, is achieved through symmetry analysis. The analytic results, together with illustrative wave interactions, show interesting physical features, that may shed some light on the study of other variable-coefficient nonlinear systems.