Scattering of waves by periodically moving bodies

Abstract

We consider solutions of the scalar wave equation vanishing on the boundary of an obstacle which undergoes periodic motion. In analogy with the Lax-Phillips theory, we show that the scattering matrix, as a function of frequency, is holomorphic in a lower half-plane, and meromorphic in an upper half-plane, provided rays are not trapped. The poles of the scattering matrix correspond to certain outgoing eigenfunctions, and there is a near-field expansion of finite energy solutions in terms of these eigenfunctions.