About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half-space, of which the cross-section is a local perturbation of a homogeneous half-plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves propagating more rapidly than S-waves. Thanks to the boundary of the deformed half-plane and some reduced equations, these eventual eigenmodes must locally vanish. Adapting to our case a unique continuation principle for the elasticity system, we conclude that these eigenmodes vanish everywhere. Copyright ? 2002 John Wiley & Sons, Ltd.