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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 426, Pages 49–63 (Mi znsl6031)  
This article is cited in 4 scientific papers (total in 4 papers)

Matching of local asymptotics in the illuminated part of Fock domain

N. Ya. Kirpichnikova, M. M. Popov

St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (226 kB) Citations (4)
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Abstract: Exploration of shortwave diffraction by elongated bodies of revolution requires detail consideration of matching of the local asymptotics in the illuminated part of Fock domain. In the paper we solve that task by means of the direct construction of the reflected wave with the help of the ray method. The main problem on that way, which was estimated by V. A. Fock as rather complicated, is the calculation of the eikonal and geometrical spreading in curvilinear coordinates used in the boundary layer method in the vicinity of light-shadow zone.
Key words and phrases: short wave diffraction by an elongated body of revolution, ray method, Fock's domain, matching of local asymptotics.
Received: 01.10.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 3, Pages 277–286
DOI: https://doi.org/10.1007/s10958-016-2777-2
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: N. Ya. Kirpichnikova, M. M. Popov, “Matching of local asymptotics in the illuminated part of Fock domain”, Mathematical problems in the theory of wave propagation. Part 44, Zap. Nauchn. Sem. POMI, 426, POMI, St. Petersburg, 2014, 49–63; J. Math. Sci. (N. Y.), 214:3 (2016), 277–286
Citation in format AMSBIB
\Bibitem{KirPop14}
\by N.~Ya.~Kirpichnikova, M.~M.~Popov
\paper Matching of local asymptotics in the illuminated part of Fock domain
\inbook Mathematical problems in the theory of wave propagation. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 426
\pages 49--63
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6031}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485305}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 3
\pages 277--286
\crossref{https://doi.org/10.1007/s10958-016-2777-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960425341}
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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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