Conservation laws and symmetries of a generalized Kawahara equation

TL;DR

This paper classifies conservation laws and symmetries of a generalized Kawahara equation, revealing their connection via Hamiltonian structure and Noether's theorem, applicable to various physical models.

Contribution

It provides a complete classification of low-order conservation laws and point symmetries for the generalized Kawahara equation, including the standard form.

Findings

Classification of low-order conservation laws and symmetries

Connection between conservation laws and symmetries via Hamiltonian structure

Application to physical models with the Kawahara equation

Abstract

The generalized Kawahara equation $u_t=a(t) u_{xxxxx} +b(t)u_{xxx} +c(t)f(u) u_x$ appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation $u_t = \alpha u u_x+\beta u^2u_x +\gamma u_{xxx}+\mu u_{xxxxx}$. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.