Nonclassical symmetry and Riemann invariants

TL;DR

This paper demonstrates that Riemann invariants remain invariant under nonclassical symmetries in hyperbolic systems, exemplified by the one-dimensional shallow water equations, revealing new invariance properties.

Contribution

It introduces the concept that Riemann invariants are invariant under nonclassical symmetries, expanding understanding of symmetries in hyperbolic systems.

Findings

Riemann invariants are invariant under nonclassical symmetries.

Application to shallow water equations shows new invariance types.

Provides a framework for analyzing symmetries in hyperbolic PDEs.

Abstract

In this paper it is shown that Riemann invariants are invariant under nonclassical symmetries of a hyperbolic system. As a specific example, we study the one-dimensional shallow water equations on the flat and present another type invariance under nonclassical symmetries.