Solitary Rayleigh waves in the presence of surface nonlinearities

The propagation of Rayleigh waves is investigated in a solid substrate of linear material covered by a film consisting of a material with large nonlinear elastic moduli. For this system, a nonlinear evolution equation is derived that may be regarded as a special case in a wider class of evolution equations with a specific type of nonlocal nonlinearity. Periodic pulse train solutions are computed. For a certain member of the class of nonlinear evolution equations, several families of solitary wave solutions and their associated periodic stationary wave solutions are derived analytically.