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

S. A. Nazarov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1092-1108

Résumé

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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