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Mathematical Analysis of Guided Water Waves

In this article, the authors consider the problem of three-dimensional linear water waves that are guided along the coast. The problem is reduced to a two-dimensional eigenvalue problem for a family of unbounded selfadjoint operators with noncompact resolvent. Questions are investigate concern-ing the existence, number, and properties of the guided modes, with particular attention given to low- and high-frequency behaviour. The authors point out a large variety of results that greatly depend on the geometry of the bottom relief.