Geodesic
On the radiation damping of whispering gallery modes for the boundaries with a strongly changing radius of curvature
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 149-151 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of the radiation damping of whispering gallery modes is considered. It is shown, that fox a prolate elliptic boundary the complex ray solution coincides locally with the asymptotics of exact eigen function. A class of boundaries is pointed, for which a complex ray method is valid. 
@article{ZNSL_1983_128_a15,
     author = {E. L. Silakov},
     title = {On the radiation damping of whispering gallery modes for the boundaries with a~strongly changing radius of curvature},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--151},
     year = {1983},
     volume = {128},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a15/}
}
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E. L. Silakov. On the radiation damping of whispering gallery modes for the boundaries with a strongly changing radius of curvature. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 149-151. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a15/