Geodesic
Tsunami waveguides
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 111-124

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We show that the submerged ridges that are periodic (in one direction), chains of submerged mountains and islands possess waveguide properties for long waves. We state a boundary value problem whose generalized eigensolutions describe the generalized eigenwaves on the fluid surface localized near the structure. We show the existence of generalized eigensolutions and eigenwaves localized near a periodic structure above or below the surface. We prove that in a neighborhood of zero there exists a pass band. We study resonance phenomena near periodic in one direction tsunami waveguides and show that two types of resonance phenomena may occur in these problems: spatially localized and synchrophasotronic.
Keywords: waveguide, periodic structures, spectral properties of the Laplacian
Mots-clés : tsunami. 
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     author = {S. V. Sukhinin and V. S. Yurkovskiǐ},
     title = {Tsunami waveguides},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {111--124},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a10/}
}
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S. V. Sukhinin; V. S. Yurkovskiǐ. Tsunami waveguides. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 111-124. http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a10/