Geodesic
Short wave point source near a~unhomogenous halfplane
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 107-120

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We consider the diffraction of waves produced by a point source by unhomogenous halfplane. The square of wave-number inside unhomogenous region is supposed to decrease lineary with increasing the distance from the devision boundary. The main aim of the article is to obtain the asymptotic of a whispering gallery waves as $k\to\infty$, where $k$ is the wave-number in a homogenous region. 
@article{ZNSL_2012_409_a6,
     author = {A. A. Matskovskiy},
     title = {Short wave point source near a~unhomogenous halfplane},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {107--120},
     publisher = {mathdoc},
     volume = {409},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a6/}
}
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A. A. Matskovskiy. Short wave point source near a~unhomogenous halfplane. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 107-120. http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a6/