Existence of eigenvalues of a linear operator pencil in a curved waveguide -- localized shelf waves on a curved coast

Details Existence of eigenvalues of a linear operator pencil in a curved waveguide -- localized shelf waves on a curved coast Existence of eigenvalues of a linear operator pencil in a curved waveguide -- localized shelf waves on a curved coast

2004-09-29

arxiv.org/abs/math/0409575v1

Mathematics

Spectral Theory

21 pages, 1 figure

Scientific paper

The study of the possibility of existence of the non-propagating, trapped continental shelf waves (CSWs)along curved coasts reduces mathematically to a spectral problem for a self-adjoint operator pencil in a curved strip. Using the methods developed in the setting of the waveguide trapped mode problem, we show that such CSWs exist for a wide class of coast curvature and depth profiles.

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