Geodesic
Asymptotics of the field diffracted on a smooth convex body near the edge of a nonsingular coustic
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 6-19

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The standard problem method is applied to construct the acoustic field asymptotics near the edge of the caustic formed by a wave diffracted on a smooth body. The field is represented by a Fresnel part and a background. Explicit formulas for the terms being a submitance of the Fresnel part and the background are obtained. Analiticity of these terms is proved. 
@article{ZNSL_1988_173_a0,
     author = {I. V. Andronov},
     title = {Asymptotics of the field diffracted on a smooth convex body near the edge of a nonsingular coustic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {6--19},
     publisher = {mathdoc},
     volume = {173},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a0/}
}
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I. V. Andronov. Asymptotics of the field diffracted on a smooth convex body near the edge of a nonsingular coustic. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 6-19. http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a0/