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: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120210915X |
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| _version_ | 1832549893616435200 |
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| author | Arthur D. Gorman |
| author_facet | Arthur D. Gorman |
| author_sort | Arthur D. Gorman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e1e87473a1fa4c24a8949230da566a16 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e1e87473a1fa4c24a8949230da566a162025-02-03T06:08:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131529129910.1155/S016117120210915XOn the time-dependent parabolic wave equationArthur D. Gorman0Department of Mathematics, Lafayette College, Easton 18042, PA, USAOne 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.http://dx.doi.org/10.1155/S016117120210915X |
| spellingShingle | Arthur D. Gorman On the time-dependent parabolic wave equation International Journal of Mathematics and Mathematical Sciences |
| title | On the time-dependent parabolic wave equation |
| title_full | On the time-dependent parabolic wave equation |
| title_fullStr | On the time-dependent parabolic wave equation |
| title_full_unstemmed | On the time-dependent parabolic wave equation |
| title_short | On the time-dependent parabolic wave equation |
| title_sort | on the time dependent parabolic wave equation |
| url | http://dx.doi.org/10.1155/S016117120210915X |
| work_keys_str_mv | AT arthurdgorman onthetimedependentparabolicwaveequation |