Theory for the time evolution of nonlinear Rayleigh waves in an isotropic solid

The evolution equations for the Rayleigh wave are derived with a single physical assumption that the cumulative effect of weak nonlinear interactions leads to a slow variation of the wave both in time and space. This solution of a classical problem of elasticity theory reveals that along with wave spectrum broadening induced by nonlinear processes (also characteristic of plane bulk pressure waves), wave spectrum narrowing may be induced by the additional nonlinear processes resulting from Rayleigh wave confinement near the surface.