Spectral gaps for water waves above a corrugated bottom | Zendy

Valeria Chiadò Piat | Zendy; С. А. Назаров | Zendy; K. Ruotsalainen | Zendy

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Spectral gaps for water waves above a corrugated bottom

Author(s) -

Valeria Chiadò Piat,

С. А. Назаров,

K. Ruotsalainen

Publication year - 2012

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2012.0545

Subject(s) - spectrum (functional analysis) , position (finance) , channel (broadcasting) , wavelength , layer (electronics) , geometry , mathematics , mathematical analysis , geology , physics , optics , telecommunications , computer science , materials science , nanotechnology , quantum mechanics , finance , economics

In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell

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