Explicit models for elastic and piezoelastic surface waves

Explicit models for the Rayleigh and Bleustein–Gulyaev surface waves are extracted from the original 2D formulations within the general framework of linear elasticity and electroelasticity. The derivations are based on perturbing in slow time the self-similar solutions for homogeneous surface wave. Both the proposed models involve hyperbolic equations on the surface along with elliptic equations over the interior, emphasizing the dual nature of a surface wave. Comparisons with exact solutions are presented, including that for the plane Lamb problem.