NONLINEAR SURFACE ELASTIC-WAVES IN A DISCRETE MODEL

The influence of nonlinearity on surface elastic waves is studied in the framework of a simple lattice model for cubic crystals including nonlinear interactions between the first, second, and third neighbors. It is shown that in the model nonlinear effects are of the same order as the dispersion ones and they may change the penetration length of surface waves. In particular, nonlinearity may support surface waves not existing in linear theory. Analytical results are obtained in two limit cases: deeply penetrating nonlinear surface waves and nonlinear waves strongly localized at the crystal surface. It is predicted that surface waves may be totally localized at the surface layer when the nonlinearity is of a certain critical value.