Geodesic
Combined method of calculation of the field of the point source in a~waveguide. (Slightly curred media)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 225-234

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The two-dimensional problem of propagation of waves, raised by a point source, in an slightly curred waveguide is investigated. The Dirichlet condition is given on the bound of the wave guide and also two junction condition are defined on the interface between fluid and bottom. The velocity is supposed to be arbitrary depending with respect to the depth of the waveguide and to be weakly depending with respect to trace coordinate. With help of cumbersome transformation the solution is represented as a sum of the geometro-optical waves, the normal waves and the residual is shown. The sufficient conditions on the general amount of the detached normal and geometro-optical waves are obtained. 
@article{ZNSL_2004_308_a12,
     author = {V. B. Philippov and N. Ya. Kirpichnikova and N. G. Vlasjuk},
     title = {Combined method of calculation of the field of the point source in a~waveguide. {(Slightly} curred media)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {225--234},
     publisher = {mathdoc},
     volume = {308},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a12/}
}
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V. B. Philippov; N. Ya. Kirpichnikova; N. G. Vlasjuk. Combined method of calculation of the field of the point source in a~waveguide. (Slightly curred media). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 225-234. http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a12/