Spectral gaps and non-Bragg resonances in a water channel

  • Valeria Chiadò Piat

    Politecnico di Torino, Italy
  • Sergei A. Nazarov

    St. Petersburg State University; Institute for Problems of Mechanical Engineering RAS, St. Petersburg, Russia
  • Keijo M. Ruotsalainen

    University of Oulu, Finland


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.

Cite this article

Valeria Chiadò Piat, Sergei A. Nazarov, Keijo M. Ruotsalainen, Spectral gaps and non-Bragg resonances in a water channel. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 2, pp. 321–342

DOI 10.4171/RLM/809