Bifurcation of the nanostructures induced by ion bombardment

We consider ion-bombardment-induced processes for formation of periodic structures. As a mathematical model, we have chosen the generalized two-dimensional Kuramoto–Sivashinsky equation which is equivalent to the equation obtained by Bradley–Harper. The jagged relief obtained due to ionic bombardment can be explained from a mathematical point of view as local bifurcations of flat profile involving an exchange of stabilities.
To describe the above relief asymptotic formulas are obtained. The bifurcation theory method for problems with infinite dimensional phase space is used to study nonlinear boundary value problem. In particular, we use normal form building which springs from Krylov–Bogolyubov method of averaging.