On the time-dependent parabolic wave equation
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 devel...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120210915X |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |