The point spectrum of the water-wave problem in intersecting channels (Q393350)

The spectral problem of the linear theory of surfaces waves is considered, for the study of trapped modes on the wave surfaces in intersecting channels. An equivalent variational problem is introduced, leading to an abstract spectral equation. The main point is to find a sufficient condition for the appearance of an eigenvalue. The method of artificial boundary conditions is used to overcome the lack of the discrete spectrum of the considered problem. A brief review of known result in the field and some open problems are given in the last part.