Conditionally invariant solutions of the rotating shallow water wave equations

TL;DR

This paper extends the conditional symmetry method to analyze and construct new solutions for the rotating shallow water wave equations, revealing classes of solutions involving arbitrary functions of Riemann invariants.

Contribution

It introduces an extension of the conditional symmetry method to nonhomogeneous systems and systematically constructs new solutions for the rotating shallow water equations.

Findings

Derived rank-1 and rank-2 solutions for shallow water equations

Constructed solutions involving arbitrary functions of Riemann invariants

Identified new classes of solutions with potential physical relevance

Abstract

This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We perform a systematic analysis of the rank-1 and rank-2 solutions admitted by the shallow water wave equations in (2 + 1) dimensions and construct the corresponding solutions of the rotating shallow water wave equations. These solutions involve in general arbitrary functions depending on Riemann invariants, which allow us to construct new interesting classes of solutions.