Symmetries and conservation laws for a generalization of Kawahara equation

TL;DR

This paper classifies symmetries and conservation laws of a generalized Kawahara equation, revealing it lacks generalized symmetries and is not symmetry integrable, with implications for plasma and water wave studies.

Contribution

It provides a complete classification of symmetries and conservation laws for a generalized Kawahara equation, showing its non-integrability.

Findings

No genuinely generalized symmetries found

Finite number of local conservation laws

Equation is not symmetry integrable

Abstract

We provide a complete classification of generalized and formal symmetries and local conservation laws for an evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and capillary-gravity water waves. In particular, we show that the equation under study admits no genuinely generalized symmetries and has only finitely many local conservation laws, and thus this equation is not symmetry integrable.