This article is cited in 35 papers

Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. I

I. V. Kamotskii^a, S. A. Nazarov<sup>b

a</sup> Saint-Petersburg State University
^b Admiral Makarov State Maritime Academy

Abstract: The solution of the problem of diffraction of an acoustic plane wave by a periodic boundary for frequencies close to threshold values is studied. Wood's well-known experiments show that deviations from the threshold frequency values by a small quantity bring about drastic changes in the diffraction pattern. The asymptotic formula with respect to the small parameter $\varepsilon$ is obtained for the corresponding scattering matrix.

UDC: 517.9

MSC: 76Q05, 35P25, 35C20

Received: 08.07.1997

DOI: 10.4213/sm379

 English version: Sbornik: Mathematics, 1999, 190:1, 111–141

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