  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.
