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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 221, Pages 67–74 (Mi znsl4296)  
This article is cited in 3 scientific papers (total in 4 papers)

Diffraction of a plane wave by a narrow cone

V. M. Babicha, B. A. Samokishb, D. B. Dement'evc

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b St. Petersburg State University of Architecture and Civil Engineering
c Saint-Petersburg State University
Full-text PDF (308 kB) Citations (4)
Abstract: The problem of diffraction of a plane scalar wave by a narrow cone is considered. The shape of the cone is arbitrary. The boundary condition is the Dirichlet or Neumann one. The wave scattered by the cone vertex arises as a result of the diffraction process. The subject of this paper is to calculate the wave amplitude. If the cone is narrow, it is possible to obtain simpler approximate formulas in comparison with Smyshlayev's one. The exactness of the approximate formulas is checked numerically. The etalon is a solution in explicit form in the axially symmetric case. The calculation shows that our formula is more exact in the case of the Dirichlet boundary condition than Felsen's formula. The approximate formula is a generalization of Felsen's one for circular cone to an arbitrary narrow cone in the case of the Neumann boundary condition. Bibliography: 6 titles.
Received: 20.01.1995
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 87, Issue 2, Pages 3311–3315
DOI: https://doi.org/10.1007/BF02355583
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. M. Babich, B. A. Samokish, D. B. Dement'ev, “Diffraction of a plane wave by a narrow cone”, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Zap. Nauchn. Sem. POMI, 221, POMI, St. Petersburg, 1995, 67–74; J. Math. Sci. (New York), 87:2 (1997), 3311–3315
Citation in format AMSBIB
\Bibitem{BabSamDem95}
\by V.~M.~Babich, B.~A.~Samokish, D.~B.~Dement'ev
\paper Diffraction of a~plane wave by a~narrow cone
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 221
\pages 67--74
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4296}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1359749}
\zmath{https://zbmath.org/?q=an:0937.35513|0900.35279}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 2
\pages 3311--3315
\crossref{https://doi.org/10.1007/BF02355583}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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