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On the time-dependent parabolic wave equation

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  • Arthur D. Gorman

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.

Suggested Citation

  • Arthur D. Gorman, 2002. "On the time-dependent parabolic wave equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:290527
    DOI: 10.1155/S016117120210915X
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