Geodesic
Whispering gallery waves in a neighborhood of a flat point of a concave boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 203-210 Cet article a éte moissonné depuis la source Math-Net.Ru

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The propagation of whispering gallery waves near a concave (from the side of the wave field) boundary having a flat point is studied. As in [4], the problem that arises for an equation of Schrodinger type is solved by the method of grids. The results of the computations are presented as shadow figures. 
@article{ZNSL_1978_78_a14,
     author = {M. M. Popov and I. Pshenchik},
     title = {Whispering gallery waves in a neighborhood of a flat point of a concave boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {203--210},
     year = {1978},
     volume = {78},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a14/}
}
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M. M. Popov; I. Pshenchik. Whispering gallery waves in a neighborhood of a flat point of a concave boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 203-210. http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a14/