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Radiation field of whispering gallery waves over a concave-convex boundary

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Abstract

In this work the wave field arising over a concave-convex reflecting boundary is studied in the Kirchhoff approximation. The field arises as a result of the incidence of whispering gallery waves on an inflection point of the boundary from the concave side. The shortwave asymptotics of the Kirchhoff integral are obtained which is expressed in terms of special functions in a neighborhood of the inflection point of the boundary and in a neighborhood of the tangent to the boundary at the inflection point. Diagrams are constructed that illustrate the behavior of the scattered field.

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Literature cited

  1. V. S. Buldyrev, “Propagation of whispering gallery waves over a concave-convex boundary,” in: Brief Summaries of Reports at the Seventh All-Union Symposium on Diffraction and Wave Propagation [in Russian], Vol. 1, Moscow (1977), pp. 33–36.

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Authors
  1. V. S. Buldyrev
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  2. A. I. Lanin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 49–65, 1981.

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Buldyrev, V.S., Lanin, A.I. Radiation field of whispering gallery waves over a concave-convex boundary. J Math Sci 20, 1776–1787 (1982). https://doi.org/10.1007/BF01119359

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  • DOI: https://doi.org/10.1007/BF01119359

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