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.
Solitary acoustic pulses can propagate along the surface of a coated homogeneous and inhomogeneous medium. It is shown how these nonlinear surface acoustic waves evolve out of initial pulselike conditions generated by pulsed laser excitation and how they can be monitored by optical detection. The solitary pulse shapes at the surface are computed on the basis of an evolution equation with nonlocal nonlinearity. They depend on the anisotropy of the substrate. Various approaches for the derivation of the evolution equation from nonlinear elasticity theory are critically compared. The behavior of the solitary pulses in collisions is investigated and is found to strongly depend on the linear dispersion law. The nontrivial depth dependence of these solitary pulses is also analyzed.
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