Spatially Inhomogeneous Solutions for a Modified Kuramoto–Sivashinsky Equation

Abstract

We study the periodic boundary value problem for a modified Kuramoto–Sivashinsky equation which can serve as a mathematical model describing formation of nanorelief on the surface of a planar target under the action of ion flux. We show that, as in the case of the traditional Kuramoto–Sivashinsky equation, it is possible to obtain spatially inhomogeneous solutions under the condition that the homogeneous equilibrium states can change the stability. We consider local bifurcations. We find sufficient conditions for the existence of shortwave solutions. Bibliography: 11 titles.