Geodesic
On adiabatic normal modes in a~wedge shaped sea
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 261-285

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We study a two-dimensional problem that is a model for sound propagation in a narrow water wedge near the shore of a sea. We explicitly construct a solution to the Helmholtz equation that is asymptotically a normal wave propagating along “water” wedge to the “shore”. The solution satisfies the Helmholtz equation in the quadrant one side of which is “the surface of the water”, and the second is perpendicular to it, starts at the top of the wedge and goes into the “bottom”. Boundary conditions at wedge boundaries and at infinity in the “bottom” are satisfied. 
@article{ZNSL_2018_471_a14,
     author = {A. A. Fedotov},
     title = {On adiabatic normal modes in a~wedge shaped sea},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {261--285},
     publisher = {mathdoc},
     volume = {471},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a14/}
}
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A. A. Fedotov. On adiabatic normal modes in a~wedge shaped sea. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 261-285. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a14/