Amplitude equations for non-linear Rayleigh waves

We investigate asymptotic equations describing small amplitude surface elas tic waves in the half-plane (Rayleigh waves). For hyperelastic materials su ch model equations are Hamiltonian systems, and are seen to lead to the for mation of singularities in the surface elastic displacement. At the time of singularity formation the Fourier spectra of the solutions exhibit power l aw decay, and the observed exponents suggest the existence of both differen tiable and non-differentiable singular profiles. (C) 2001 Elsevier Science B.V. All rights reserved.