Geodesic
Wood's anomalies and surface waves in the problem of scattering by a~periodic boundary.~II
Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 205-231

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The solution of the problem of diffraction of an acoustic plane wave by a periodic boundary for frequencies close to threshold values is studied. It is shown that if the periodic structure has some special geometry, then the transformations of the diffraction pattern (Wood's anomalies) are accompanied by the occurrence of surface waves. Substantiation of asymptotic formulae (in particular, the ones in [1]) is carried out on the basis of the techniques of equivalent weighted norms in Sobolev spaces. 
@article{SM_1999_190_2_a2,
     author = {I. V. Kamotskii and S. A. Nazarov},
     title = {Wood's anomalies and surface waves in the problem of scattering by a~periodic {boundary.~II}},
     journal = {Sbornik. Mathematics},
     pages = {205--231},
     publisher = {mathdoc},
     volume = {190},
     number = {2},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_2_a2/}
}
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I. V. Kamotskii; S. A. Nazarov. Wood's anomalies and surface waves in the problem of scattering by a~periodic boundary.~II. Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 205-231. http://geodesic.mathdoc.fr/item/SM_1999_190_2_a2/