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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 6, Pages 1092–1108 (Mi zvmmf4893)  

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

Formation of gaps in the spectrum of the problem of waves on the surface of a periodic channel

S. A. Nazarov

Institute of Problems of Machine Science, Russian Academy of Sciences, Vasil'evskii Ostrov, Bol'shoi pr. 61, St. Petersburg, 199178 Russia

Abstract: It is shown that the essential spectrum of a problem in the theory of linear water waves in a periodic channel can contain any prescribed number of gaps. One of such waveguides consists of a periodic family of identical ponds of unit size connected by narrow shallow channels. The effect of gap opening is achieved by decreasing a geometric parameter describing the size of these channels.

Key words: linear water wave theory, essential spectrum, gaps in spectrum.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:6, 1038–1054

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 03.06.2009

Citation: S. A. Nazarov, “Formation of gaps in the spectrum of the problem of waves on the surface of a periodic channel”, Zh. Vychisl. Mat. Mat. Fiz., 50:6 (2010), 1092–1108; Comput. Math. Math. Phys., 50:6 (2010), 1038–1054

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Piat V.Ch., Nazarov S.A., Ruotsalainen K., “Spectral Gaps for Water Waves Above a Corrugated Bottom”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 469:2149 (2013), 20120545  crossref  mathscinet  zmath  isi  elib  scopus
    2. Bakharev F.L., Ruotsalainen K., Taskinen J., “Spectral Gaps For the Linear Surface Wave Model in Periodic Channels”, Q. J. Mech. Appl. Math., 67:3 (2014), 343–362  crossref  mathscinet  zmath  isi  elib  scopus
    3. Piat V.Ch., Nazarov S.A., Ruotsalainen K.M., “Spectral Gaps and Non-Bragg Resonances in a Water Channel”, Rend. Lincei-Mat. Appl., 29:2 (2018), 321–342  crossref  mathscinet  zmath  isi  scopus
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