Group classification and conservation laws for a two-dimensional generalized Kuramoto–Sivashinsky equation

The two-dimensional anisotropic Kuramoto–Sivashinsky equation is a fourth-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.