Geodesic
Interference head wave in the problem of wave diffraction on homogenous halfplane
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 140-149

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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 linearly with increasing the distance from the division boundary. Using the results obtained in [11] the Buldyrev head wave and whispering gallery waves structure analysis is performed. 
@article{ZNSL_2014_426_a9,
     author = {A. A. Matskovskiy},
     title = {Interference head wave in the problem of wave diffraction on homogenous halfplane},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--149},
     publisher = {mathdoc},
     volume = {426},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a9/}
}
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A. A. Matskovskiy. Interference head wave in the problem of wave diffraction on homogenous halfplane. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 140-149. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a9/