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"Bottom crystal" and possibility of water wave attenuation

Popov I. Yu

Archives of Mechanics

2003

Vol. 55, nr 2

221-232

The influence of periodic bottom structure ("bottom crystal'') on surface water waves is considered. The problem reduces to a two-dimensional Helmholtz operator with periodic potential. Zero-range potential method based on the theory of self-adjoint extensions of symmetric operators is used. It is shown that there is a gap in the spectrum. An application of this spectral property to the problem of wave attenuation is discussed.