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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 426, Pages 87–118 (Mi znsl6033)  
This article is cited in 4 scientific papers (total in 4 papers)

Parabolic equation method and Fresnel approximation in Weinstein's problems

A. I. Korol'kov, A. V. Shanin

M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russia
Full-text PDF (300 kB) Citations (4)
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Abstract: A problem of diffraction of a high frequency plane wave by a grating, consisting of absorbing screens is studied. Difficulties of a correct mathematical formulation of the problem are addressed. It is shown how this problem is connected with the classical Weinstein's problem of scattering by an open end of a planar waveguide. All results are derived by two different approaches: by the parabolic equation approach and by the method of Fresnel integrals. The equivalence of these approaches allows one to use Fresnel integrals for rigorous reasoning keeping the parabolic equation method for clear physical understanding of the results obtained.
Key words and phrases: diffraction grating, absorbing screens, parabolic equation.
Received: 28.10.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 3, Pages 302–321
DOI: https://doi.org/10.1007/s10958-016-2779-0
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. I. Korol'kov, A. V. Shanin, “Parabolic equation method and Fresnel approximation in Weinstein's problems”, Mathematical problems in the theory of wave propagation. Part 44, Zap. Nauchn. Sem. POMI, 426, POMI, St. Petersburg, 2014, 87–118; J. Math. Sci. (N. Y.), 214:3 (2016), 302–321
Citation in format AMSBIB
\Bibitem{KorSha14}
\by A.~I.~Korol'kov, A.~V.~Shanin
\paper Parabolic equation method and Fresnel approximation in Weinstein's problems
\inbook Mathematical problems in the theory of wave propagation. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 426
\pages 87--118
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485307}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 3
\pages 302--321
\crossref{https://doi.org/10.1007/s10958-016-2779-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960339132}
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  • https://www.mathnet.ru/eng/znsl/v426/p87
    • 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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