On the Theory of Complex Rays
The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredien...
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| Veröffentlicht in: | SIAM review 1999-09, Vol.41 (3), p.417-509 |
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| container_title | SIAM review |
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| creator | Chapman, S. J. Lawry, J. M. H. Ockendon, J. R. Tew, R. H. |
| description | The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredient in this framework is the role played by Stokes' phenomenon in determining the regions of existence of complex rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel-Kramers-Brilbuin expansion of these wavefields. Examples are given for several cases of physical importance. |
| doi_str_mv | 10.1137/S0036144599352058 |
| format | Article |
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The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel-Kramers-Brilbuin expansion of these wavefields. Examples are given for several cases of physical importance.</description><subject>Acoustics</subject><subject>Approximation</subject><subject>Caustic networks</subject><subject>Coordinate systems</subject><subject>Cylinders</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Geometrical optics</subject><subject>Geometry</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Optics</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Plane waves</subject><subject>Riemann surfaces</subject><subject>Sciences and techniques of general use</subject><subject>Sine function</subject><subject>Survey and Review</subject><subject>Tangents</subject><subject>Underwater sound</subject><subject>Wave diffraction</subject><subject>Wave reflection</subject><issn>0036-1445</issn><issn>1095-7200</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNplUFtLwzAUDqLgnP4AQaGIr9Vzcpo0eZThDQYDnc8liwnb6JqZdGD_vS0b-uDT4fBd-Ri7RLhDpPL-HYAkFoXQmgQHoY7YCEGLvOQAx2w0wPmAn7KzlNbQ_4r0iF3Pmqxdumy-dCF2WfDZJGy2tfvO3kyXztmJN3VyF4c7Zh9Pj_PJSz6dPb9OHqa5JQ5tTsoWBEaTVtIgLJAWJUjhnQJLZV9LaKeMBiTtLefaeo9FT_lclCSFQBqzm73vNoavnUtttQ672PSRFeqCg5J93zHDPcnGkFJ0vtrG1cbErkKohhGqfyP0mtuDsUnW1D6axq7Sn1BL0OWQf7WnrVMb4i_MpSAuC_oBKSVgrg</recordid><startdate>19990901</startdate><enddate>19990901</enddate><creator>Chapman, S. 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| ispartof | SIAM review, 1999-09, Vol.41 (3), p.417-509 |
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| language | eng |
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| source | JSTOR Mathematics & Statistics; EBSCOhost Business Source Complete; JSTOR Archive Collection A-Z Listing; LOCUS - SIAM's Online Journal Archive |
| subjects | Acoustics Approximation Caustic networks Coordinate systems Cylinders Exact sciences and technology Fundamental areas of phenomenology (including applications) Geometrical optics Geometry Mathematical analysis Mathematics Optics Partial differential equations Physics Plane waves Riemann surfaces Sciences and techniques of general use Sine function Survey and Review Tangents Underwater sound Wave diffraction Wave reflection |
| title | On the Theory of Complex Rays |
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