© Hindawi Publishing Corp. ON THE TIME-DEPENDENT PARABOLIC WAVE EQUATION

One approach to the study of wave propagation in a restricted domain is to approximate the reducedHelmholtz equation by a parabolic wave equation. Herewe consider wave prop-agation in a restricted domain modelled by a parabolic wave equation whose properties vary both in space and in time. We develop a Wentzel-Kramers-Brillouin (WKB) formalism to obtain the asymptotic solution in noncaustic regions and modify the Lagrange manifold formalism to obtain the asymptotic solution near caustics. Associated wave phenomena are also considered. 2000 Mathematics Subject Classification: 34E20