Geodesic
The point spectrum of water-wave problem in intersecting canals
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 40, Tome 380 (2010), pp. 110-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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Trapped modes are examined on the water surface in two canals which intersect each other at the right angle and have the same symmetric cross-section. These trapped modes correspond to eigenvalues embedded into the continuous spectrum of the Steklov boundary value problem, decay exponentially at infinity, i.e., are localized near the crossing of the canals. A sufficient condition is presented for the existence of such trapped waves. The effect is discussed of the concentration of eigenvalues under a perturbation in the vicinity of the canals crossing by means of the formation of a shoal, a thin water layer. A condensed review of known results on curved, cranked and branched waveguides is given and open questions are formulated. Bibl. 24 titles. 
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     title = {The point spectrum of water-wave problem in intersecting canals},
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S. A. Nazarov. The point spectrum of water-wave problem in intersecting canals. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 40, Tome 380 (2010), pp. 110-131. http://geodesic.mathdoc.fr/item/ZNSL_2010_380_a6/

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