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The asymptotic analysis of canonical problems in high-frequency scattering theory

I. Stratified media above a plane boundary

Published online by Cambridge University Press:  24 October 2008

W. G. C. Boyd
W. G. C. Boyd
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN
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Abstract

The asymptotic treatment of high-frequency scalar wave problems has in the past been rather unsatisfactory. Typically, the integral representations which arose were evaluated by stationary phase, or as a series of residues. The justification of these methods was usually heuristic and formal. In this paper, a method is advanced which, it is claimed, may be applied to any one-parameter separation of variables problem. The method assumes an integral representation whose contour of integration is the real axis. It is then only necessary to deform this contour in the neighbour-hood of the real axis to derive rigorous asymptotic expansions of the field in both the illumination and shadow. The method is applied to the particular example of scattering by a plane boundary in a general stratified medium with monotonically increasing refractive index.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 289 - 312
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

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