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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 451, Pages 156–177 (Mi znsl6351)  

This article is cited in 6 scientific papers (total in 6 papers)

On short-wave diffraction by strongly prolate body of revolution

M. M. Popov, N. M. Semtchenok, N. Ya. Kirpichnikova

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (387 kB) Citations (6)
References:
Abstract: In the paper a short-wave diffraction problem by strongly elongated body of revolution (axisymmetric case) is considered. In that case the classical method of Leontovich–Fock parabolic equation (actually Schrödinger type equation) turns out to be inapplicable due to corresponding recurrent system of equations loses asymptotic character and, moreover, each equation gets singularity in coefficients, including the main parabolic equation. In the work, we introduce a new boundary layer defined by the new scaling of the internal coordinates of the layer differs from the Fock case. Unfortunately, the variables cannot be separated in the main parabolic equation and therefore it is hardly possible to construct the solution of the problem in closed analytic form. Instead, we formulated a non-stationary scattering problem for the Schrödinger type equation, where role of the time plays the arc length along the meridians, and solved it by numerical methods.
Key words and phrases: short wave diffraction, boundary layer, ray method, scattering problem for Schrödinger equation, finite difference methods.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00535-А
Received: 14.10.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 6, Pages 795–809
DOI: https://doi.org/10.1007/s10958-017-3567-1
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. M. Popov, N. M. Semtchenok, N. Ya. Kirpichnikova, “On short-wave diffraction by strongly prolate body of revolution”, Mathematical problems in the theory of wave propagation. Part 46, Zap. Nauchn. Sem. POMI, 451, POMI, St. Petersburg, 2016, 156–177; J. Math. Sci. (N. Y.), 226:6 (2017), 795–809
Citation in format AMSBIB
\Bibitem{PopSemKir16}
\by M.~M.~Popov, N.~M.~Semtchenok, N.~Ya.~Kirpichnikova
\paper On short-wave diffraction by strongly prolate body of revolution
\inbook Mathematical problems in the theory of wave propagation. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 451
\pages 156--177
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6351}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589172}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 6
\pages 795--809
\crossref{https://doi.org/10.1007/s10958-017-3567-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030224976}
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  • https://www.mathnet.ru/eng/znsl/v451/p156
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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