Space-time caustics (Q1088835)

The author considers the determination of the asymptotic solution of a kind of linear differential equation of the form \[ \nabla^ 2\psi (\bar r,t)-f(\bar r,t)\frac{\partial^ 2\psi (\bar r,t)}{\partial t^ 2}- \lambda^ 2g(\bar r,t)\psi (\bar r,t)=0, \] which models the wave propagation in media with both spatial and temporal inhomogeneities. The asymptotic solutions available away from the caustic points are found by the WKB-method; and the solutions available near the caustic points are found by the Lagrange manifold formalism. The analogous Schrödinger equation is also considered.