Geodesic
A point source of oscillations on the boundary of a region
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 3-20

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The problem of a point source of oscillations on a curve $S$ with curvature which is nowhere zero is considered: $$ w_{tt}-w_{xx}-w_{yy}=0;\quad w|_{t0}=0;\quad w|_s=\delta(s-s_0);\quad s,s_0\in S. $$ The case where the whispering gallery effect arises is investigated: rays issuing from a source $s_0\in S$ and reflected many times from $S$ create this effect. A function containing all singularities of $w$ is constructed explicitly. The theorem that the set of singularities of the function $w$ coincides with the wave fronts of geometrical optics is a consequence of these considerations. 
@article{ZNSL_1976_62_a0,
     author = {V. M. Babich},
     title = {A point source of oscillations on the boundary of a region},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {62},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a0/}
}
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V. M. Babich. A point source of oscillations on the boundary of a region. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 3-20. http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a0/