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International Journal of Mathematics and Mathematical Sciences - Volume 31 2002, Issue 5, Pages 291-299

Department of Mathematics, Lafayette College, Easton 18042, PA, USA

Received 12 September 2001

Copyright © 2002 Hindawi Publishing Corporation. 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 restricteddomain is to approximate the reduced Helmholtz equation by aparabolic wave equation. Here we consider wave propagation in arestricted domain modelled by a parabolic wave equation whoseproperties vary both in space and in time. We develop aWentzel-Kramers-Brillouin WKB formalism to obtain theasymptotic solution in noncaustic regions and modify the Lagrangemanifold formalism to obtain the asymptotic solution nearcaustics. Associated wave phenomena are also considered.

Author: Arthur D. Gorman

Source: https://www.hindawi.com/


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