Group Classification and Conservation Laws for a two-dimensional Generalized Kuramoto-Sivashinsky Equation

TL;DR

This paper performs a comprehensive symmetry analysis and classification of a generalized two-dimensional Kuramoto-Sivashinsky equation, identifying conservation laws and exploring its mathematical properties relevant to physical surface processes.

Contribution

It provides the first complete group classification of the generalized equation, linking symmetry properties to conservation laws and self-adjointness.

Findings

Complete group classification achieved

Conservation laws established for the generalized equation

Analysis of self-adjointness properties

Abstract

The two-dimensional anisotropic Kuramoto-Sivashinsky equation is a forth-order nonlinear evolution equation in two spatial dimensions that arises in sputter erosion and epitaxial growth on vicinal surfaces. A generalization of this equation is proposed and studied via group analysis methods. The complete group classification of this generalized Kuramoto-Sivashinsky equation is carried out, it is classified according to the property of the self-adjointness and the corresponding conservation laws are established.