Geodesic
Combined method calculating the field generated by a~point source in a~surface wave guide
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 110-120

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The two-dimensional problem of propagation of waves, raised by a point source, in an interior layer wave guide is investigated. The Dirichlet condition is given on the bound of the wave guide. With help of cumbersome transformation the solution is represented as a sum of the geometro-optical waves, the normal waves and the residual. The sufficient conditions for the general amount of the detached normal and geometro-optical waves are obtained. The residual is expressed by the simple formula. 
@article{ZNSL_2005_324_a5,
     author = {N. Ya. Kirpichnikova and V. B. Philippov and S. Yu. Fadeeva},
     title = {Combined method calculating  the field generated by a~point source in a~surface wave guide},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--120},
     publisher = {mathdoc},
     volume = {324},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a5/}
}
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N. Ya. Kirpichnikova; V. B. Philippov; S. Yu. Fadeeva. Combined method calculating  the field generated by a~point source in a~surface wave guide. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 110-120. http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a5/