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Opening gaps in the spectrum of the water-wave problem in a periodic channel

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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.

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Authors and Affiliations

  1. Institute of Problems in Machine Science, Russian Academy of Sciences, Vasil’evskii Ostrov, Bol’shoipr. 61, St. Petersburg, 199178, Russia

    S. A. Nazarov

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Correspondence to S. A. Nazarov.

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Original Russian Text © S.A. Nazarov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 6, pp. 1092–1108.

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Nazarov, S.A. Opening gaps in the spectrum of the water-wave problem in a periodic channel. Comput. Math. and Math. Phys. 50, 1038–1054 (2010). https://doi.org/10.1134/S0965542510060102

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