Singularity phenomena in ray propagation in anisotropic media

Propagation of acoustic waves at a high frequency in anisotropic media is considered. In this case, the WKB approximation results in eikonal equations whose Hamiltonians are neither convex nor concave in the impulse variable as it is the case in differential games theory. In this paper the methods of differential games are adopted for the analysis of wave propagation. If the Hamiltonian of a differential game approximates the Hamiltonian of the eikonal equation, then the solution to the game approximates the phase function satisfying the eikonal equation. The method of singular characteristics is used for the analysis of singularities in associated differential games. Numerical results are presented for wave velocity surfaces typical for anisotropic quartz crystals.