Geodesic
Excitation coefficients of the whispering gallery waves in a vicinity of concave boundary with curvature vanishing at a point
Zapiski Nauchnykh Seminarov POMI, Interference waves in layered media. Part I, Tome 99 (1980), pp. 138-145 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method is presented for computing the excitation coefficients of whispering gallery waves arising behind a given point, at which the curvature of the concave boundary vanishes. Absolute values of some coefficients for the incident whispering gallery waves No 1 and No 2 are computed. It follows from these results that the principal part of the incident wave energy in both cases is transformed into the whispering gallery wave No 1. 
@article{ZNSL_1980_99_a12,
     author = {V. G. Krasavin and M. M. Popov},
     title = {Excitation coefficients of the whispering gallery waves in a~vicinity of concave boundary with curvature vanishing at a~point},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--145},
     year = {1980},
     volume = {99},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_99_a12/}
}
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V. G. Krasavin; M. M. Popov. Excitation coefficients of the whispering gallery waves in a vicinity of concave boundary with curvature vanishing at a point. Zapiski Nauchnykh Seminarov POMI, Interference waves in layered media. Part I, Tome 99 (1980), pp. 138-145. http://geodesic.mathdoc.fr/item/ZNSL_1980_99_a12/