Geodesic
Direction diagram of radiation in the problem of an inflection point of the boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 167-173 Cet article a éte moissonné depuis la source Math-Net.Ru

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The coefficient of the first term of the ray asymptotics in this problem is computed for the first three whispering-gallery waves incident on a point of rectification of the boundary. 
@article{ZNSL_1984_140_a14,
     author = {V. G. Krasavin and M. M. Popov},
     title = {Direction diagram of radiation in the problem of an inflection point of the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--173},
     year = {1984},
     volume = {140},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a14/}
}
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V. G. Krasavin; M. M. Popov. Direction diagram of radiation in the problem of an inflection point of the boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 167-173. http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a14/