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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 451, Pages 188–207 (Mi znsl6353)  

This article is cited in 3 scientific papers (total in 3 papers)

Boundary integral equation and the problem of diffraction on a curved surface for the parabolic equation of the diffraction theory

A. V. Shanin, A. I. Korol'kov

Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (258 kB) Citations (3)
References:
Abstract: The two-dimensional problem of diffraction on a curved surface for the parabolic equation of the diffraction theory is considered. Ideal boundary conditions is satisfied on the surface. The boundary integral equation of Volterra type is introduced. Using the latter the problem of diffraction on parabola is analyzed. It is shown that solution of this problem coincides with the Fock asymptotic solution for cylinder. Also the iterative solution of the boundary integral equation is constructed. The problem of diffraction on a perturbation of a straight line is solved numerically using the boundary integral equation. It is showed that this numerical approach is relatively cheap.
Key words and phrases: boundary integral equation method, parabolic equation, diffraction on a curved surfaces, Fock's integral.
Received: 15.11.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 6, Pages 817–830
DOI: https://doi.org/10.1007/s10958-017-3569-z
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. V. Shanin, A. I. Korol'kov, “Boundary integral equation and the problem of diffraction on a curved surface for the parabolic equation of the diffraction theory”, Mathematical problems in the theory of wave propagation. Part 46, Zap. Nauchn. Sem. POMI, 451, POMI, St. Petersburg, 2016, 188–207; J. Math. Sci. (N. Y.), 226:6 (2017), 817–830
Citation in format AMSBIB
\Bibitem{ShaKor16}
\by A.~V.~Shanin, A.~I.~Korol'kov
\paper Boundary integral equation and the problem of diffraction on a~curved surface for the parabolic equation of the diffraction theory
\inbook Mathematical problems in the theory of wave propagation. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 451
\pages 188--207
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6353}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589174}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 6
\pages 817--830
\crossref{https://doi.org/10.1007/s10958-017-3569-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85031498744}
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  • https://www.mathnet.ru/eng/znsl/v451/p188
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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