Keele Research Repository

In these lectures, we discuss three closely related topics. We first discuss derivation of the nonlinear evolution equation for surface acoustic waves and show that all known methods of derivation should and do give the same evolution equation. We then study linear wave propagation in a coated elastic half-space and show how the dispersion relation can be expressed elegantly in terms of the surface-impedance matrices associated with the layer and half-space. We derive a two-term expression for the wave speed in the long-wavelength limit. Finally, we look at periodic and solitary waves in a coated elastic half-space. We derive the nonlinear evolution equation for small-amplitude long-wavelength travelling waves propagating in a coated elastic half-space where the thin coating induces weak dispersion. We explain a simple method that can be used to compute periodic or solitary travelling-wave solutions.