Generalized Kuramoto-Sivashinsky equations as models
for the evolution of surface morphologies

Stefan Linz

Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Str. 9, 48149 Münster, Germany

Due to its invariance properties, the two-dimensional stochastic Kuramoto-Sivashinsky (KS) equation can be considered as the skeleton model for pattern formation of surface evolution processes. The specific physical mechanisms of the processes often requires generalizations of the KS equation in various ways in order to explain experimental findings. Taking into account the conceptional difference of growth and erosion processes, we we formally derive and discuss two distinct generalizations of the KS equation, address the physical mechanisms leading to the specific functional forms, and show that they are able to reproduce the experimentally observed morphology evolution.