Evolution of pattern formation under ion bombardment of substrate

Processes of self-organization described by a nonlinear evolution equation of sixth order are considered on substrate surfaces after ion beam bombardment. Five families of exact solutions are found for the nonlinear evolution equation. A numerical method enabling one to solve the boundary value problem is presented. Simulation of the pattern formation and classification of their profiles are given. The influence of the third, fifth order dispersion terms and a nonlinear diffusion term on processes of the pattern formation is discussed.