Geodesic
Localization of surface waves by small perturbations of the boundary of a~semisubmerged body
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 1, pp. 93-101

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It is shown under the condition of symmetry that, by means of formation of a thin groove on the planar surface of a body parallel to the liquid's horizon in a cylindrical channel, we can achieve the following effect in the linear problem concerning the waves on water: on every arbitrarily short interval $(0,d)$ of the continuous spectrum, any prescribed number of the eigenvalues is formed giving rise to “localized” solutions, i.e., belonging to a Sobolev space.
Keywords: surface wave, trapping modes, localized solution, singular perturbations of the boundary. 
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     author = {S. A. Nazarov},
     title = {Localization of surface waves by small perturbations of the boundary of a~semisubmerged body},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {93--101},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_1_a8/}
}
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S. A. Nazarov. Localization of surface waves by small perturbations of the boundary of a~semisubmerged body. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 1, pp. 93-101. http://geodesic.mathdoc.fr/item/SJIM_2011_14_1_a8/