Iterative symmetry search and reduction of a wave water model in $2+1$ dimensions

TL;DR

This paper performs an iterative symmetry analysis of a 2+1 dimensional shallow water wave model, identifying reductions linked to well-known nonlinear wave equations and examining their spectral properties.

Contribution

It introduces a novel iterative symmetry analysis method for the water wave model and its Lax pair, revealing new reductions and their spectral characteristics.

Findings

Identified several reductions related to classical nonlinear wave equations

Analyzed the isospectral and nonisospectral nature of spectral problems

Provided insights into the integrability and spectral properties of the model

Abstract

We present the iterative classical point symmetry analysis of a shallow water wave equation in $2+1$ dimensions and that of its corresponding nonisospectral, two component Lax pair. A few reductions arise and are identified with celebrate equations in the Physics and Mathematics literature of nonlinear waves. We pay particular attention to the isospectral or nonisospectral nature of the reduced spectral problems.