Abstract
The general theory of elastic waves in anisotropic media is briefly reviewed. The present status of existence considerations for surface waves is discussed. The main concepts involved in determining the resonant properties of reflection (transmission) near the leaky wave branch are introduced both for plane waves and for bounded beams. The exceptional waves and their relation to the degeneracy of phase velocities of bulk waves are discussed. Finally, the classification of acoustic axes, comprising all possible types of contact geometry of degenerate velocity sheets and the corresponding polarization singularities, is reviewed.
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