Do Surface Acoustic Solitons Exist?

Abstract

Nonlinear Rayleigh waves are considered that propagate along the surface of a homogeneous solid medium covered by a thin film. Their dynamics is described by an evolution equation containing dispersion of the Benjamin-Ono type and a nonlocal nonlinearity. Periodic nonlinear wave solutions are found which become solitary waves in the limit of infinite periodicity. It is shown that these solitary solutions are stable, but unlike the Korteweg--de Vries solitons, they do not survive collisions with each other and therefore are no real solitons.