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Journal of Mathematical Sciences

, Volume 73, Issue 3, pp 353–360 | Cite as

Wood's anomalies in the scattering problem of a plane wave on a smooth periodic boundary

  • V. V. Zalipaev
  • M. M. Popov
Article
  • 28 Downloads

Abstract

A series of multiple diffracted fields in a high-frequency asymptotic expansion of the solution to the problem of grazing scattering of a plane wave by a smooth periodic boundary is summed in the case of appearance of Wood's anomalies. Bibliography: 8 titles.

Keywords

Plane Wave Asymptotic Expansion Periodic Boundary Diffract Field Grazing Scattering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    V. V. Zalipaev and M. M. Popov, “Shortwave grazing scattering of a plane wave by a smooth periodic boundary. I,”J. Soviet Math.,50, No. 6, 1971–1993 (1990).MathSciNetGoogle Scholar
  2. 2.
    V. V. Zalipaev and M. M. Popov, “Shortwave grazing scattering of a plane wave by a smooth periodic boundary. II,”J. Soviet Math.,55, No. 3 1685–1705 (1991).MathSciNetGoogle Scholar
  3. 3.
    V. P. Shestopalov, A. A. Kirilenko, S. A. Masalov, and Yu. K. Sirenko,Resonance Scattering of Waves. Diffraction Gratings [in Russian], Vol. 1, Kiev (1986).Google Scholar
  4. 4.
    L. A. Weinstein,The theory of Diffraction and the Factorization Method, Golem Press, Boulder, CO (1969).Google Scholar
  5. 5.
    V. A. Fock,Electromagnetic Diffraction and Propagation Problems, Pergamon Press, Oxford (1965).Google Scholar
  6. 6.
    J. Boersma, “Ray-optical analysis of reflection in an open-ended parallel-plane waveguide. I: TM case,”SIAM J. Appl. Math.,29, No. 1, 164–195 (1975).MathSciNetGoogle Scholar
  7. 7.
    M. G. Krein, “Integral equation on a half-axis with kernel depending on the difference of arguments,”Usp. Math. Nauk,13, No. 5, 3–120 (1958).MATHMathSciNetGoogle Scholar
  8. 8.
    J. Boersma, “On certain multiple integrals occuring in a waveguide scattering problem,”SIAM J. Math. Anal.,9, No. 2, 377–393 (1978).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. V. Zalipaev
  • M. M. Popov

There are no affiliations available

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