International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 5, Pages 291-299
doi:10.1155/S016117120210915X

On the time-dependent parabolic wave equation

Abstract

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 we consider wave propagation 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.