On the time-dependent parabolic wave equation (Q1607946)

Summary: One approach to the study of wave propagation in a restricted domain is to approximate the reduced Helmholtz equation by a parabolic wave equation. Here, the author considers the wave propagation in a restricted domain modelled by a parabolic wave equation whose properties vary both in space and in time. He develops a Wentzel-Kramers-Brillouin (WKB) formalism to obtain an asymptotic solution in noncaustic regions and modifies the Lagrange manifold formalism to obtain an asymptotic solution near caustics. Associated wave phenomena are also considered.