Waves, Caustics and Thom's Theorem.

The technique of Maslov for determining the first term in the asymptotic series solution of linear partial differential equations is extended to determine the full asymptotic series solution of the reduced Helmholtz equation for scalar waves propagated in an inhomogeneous medium. The algorithm requires the characterization of the medium by a canonical phase function determined from a criterion derived Thom's classification of singularities.