International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 5, Pages 291-299
On the time-dependent parabolic wave equation
Department of Mathematics, Lafayette College, Easton 18042, PA, USA
Received 12 September 2001
Copyright © 2002 Arthur D. Gorman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.