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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 409, Pages 151–175 (Mi znsl5517)  
This article is cited in 1 scientific paper (total in 1 paper)

Wave Wall for waves on the surface of a heavy liquid

A. I. Popovab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
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Abstract: Asymptotic analysis of surface water waves is made. Gradient of the ocean depth is assumed small. The ansatz for the asymptotic expansion in this small parameter is suggested. The goal is to construct full asymptotic expansion for the solution localized near moving line on the liquid surface. The approach is based on space-time ray method. Eiconal and amplitudes are found in the forms of formal power series. Chains of recurrent equations for its terms are derived. Their solvability is proved. The first term is obtained in explicit form.
Key words and phrases: Wave Wall, asymptotic expansion, space-time ray method.
Received: 20.11.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 194, Issue 1, Pages 83–97
DOI: https://doi.org/10.1007/s10958-013-1509-0
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. I. Popov, “Wave Wall for waves on the surface of a heavy liquid”, Mathematical problems in the theory of wave propagation. Part 42, Zap. Nauchn. Sem. POMI, 409, POMI, St. Petersburg, 2012, 151–175; J. Math. Sci. (N. Y.), 194:1 (2013), 83–97
Citation in format AMSBIB
\Bibitem{Pop12}
\by A.~I.~Popov
\paper Wave Wall for waves on the surface of a~heavy liquid
\inbook Mathematical problems in the theory of wave propagation. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 409
\pages 151--175
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5517}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3032234}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 194
\issue 1
\pages 83--97
\crossref{https://doi.org/10.1007/s10958-013-1509-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898973884}
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  • https://www.mathnet.ru/eng/znsl/v409/p151
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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