Spectral gaps and non-Bragg resonances in a water channel
Chiadò Piat, Valeria; Nazarov, Sergey A.; Ruotsalainen, Keijo M. (2018-04-26)
Chiadò Piat Valeria, Nazarov Sergey, Ruotsalainen Keijo: Spectral gaps and non-Bragg resonances in a water channel. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 321-342. doi: 10.4171/RLM/809
© 2018 EMS Publishing House. All rights reserved. Published in this repository with the kind permission of the publisher.
In this paper the essential spectrum of the linear problem of water-waves on a 3d-channel with gently periodic bottom will be studied. We show that under a certain geometric condition on the bottom profile the essential spectrum has spectral gaps. In classical analysis of waveguides it is known that the Bragg resonances at the edges of the Brillouin zones create band gaps in the spectrum. Here we demonstrate that the band gaps can be opened also in the frequency range far from the Bragg resonances. 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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