Geodesic
Combined method of calculation of the field of the point source in a~wave guide
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 116-135

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The two-dimensional problem of propagation of waves, raised by a point source, in an interior wave guide is investigated. The Dirichlet (Neumann) boundary condition is given on the upper (lower) bound of the wave guide. The possibility of representation of the exact solution 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. The residual is expressed by the simple formula. 
@article{ZNSL_2003_297_a7,
     author = {N. Ya. Kirpichnikova and V. B. Philippov and N. G. Vlasjuk},
     title = {Combined method of calculation of the field of the point source in a~wave guide},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--135},
     publisher = {mathdoc},
     volume = {297},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a7/}
}
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N. Ya. Kirpichnikova; V. B. Philippov; N. G. Vlasjuk. Combined method of calculation of the field of the point source in a~wave guide. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 116-135. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a7/