Geodesic
Directional diagram of whispering gallery modes for сопсате reflector
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 15, Tome 148 (1985), pp. 61-67

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The short wave asymptotics of directional diagram of the wave field, scattered by nonplanar screen, which corresponds wispering gallery modes is found. She Siriehlet problem for parabolic screen is considered and the results of calculations are given. 
@article{ZNSL_1985_148_a6,
     author = {O. V. Graunov and V. B. Filippov},
     title = {Directional diagram of whispering gallery modes for {\cyrs}{\cyro}{\cyrp}{\cyrs}{\cyra}{\cyrt}{\cyre} reflector},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {61--67},
     publisher = {mathdoc},
     volume = {148},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_148_a6/}
}
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O. V. Graunov; V. B. Filippov. Directional diagram of whispering gallery modes for сопсате reflector. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 15, Tome 148 (1985), pp. 61-67. http://geodesic.mathdoc.fr/item/ZNSL_1985_148_a6/