Tsunami waveguides

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.