Period steady-state identification for a nonlinear front evolution equation using genetic algorithms

In molecular beam epitaxy, it is known that a planar surface may suffer from a morphological instability in favour to different front pattern formations. In this context, many studies turned their focus to the theoretical and numerical analysis of highly nonlinear partial differential equations which exhibit different scenarios ranging from spatio-temporal chaos to coarsening processes (i.e., an emerging pattern whose typical length scale with time). In this work our attention is addressed toward the study of a highly nonlinear front evolution equation proposed by Csahok et al. (1999) where the unknowns are the periodic steady states which play a major role in investigating the coarsening dynamics. Therefore the classical methods of Newton or a fixed point type are not suitable in this situation. To overcome this problem, we develop in this paper a new approach based on heuristic methods such as genetic algorithms in order to compute the unknowns.