Geodesic
The scattering of short waves in a vicinity of a boundary flex point
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 15, Tome 148 (1985), pp. 152-166

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The problem of an tangential incidence of short waves on a surface with a flex point is considered. Pormal solutions of the problem in the form of series of quasi-homogeneous functions in-the vicinity of flex point is constructed. The problem is formulated as a scattering one for the Schrodinger equation and theorems of existence, uniqueness and smoothness of the solution are proved. The Justification of formal asymptotics is given. 
@article{ZNSL_1985_148_a15,
     author = {V. P. Smyshlyaev},
     title = {The scattering of short waves in a vicinity of a boundary flex point},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {152--166},
     publisher = {mathdoc},
     volume = {148},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_148_a15/}
}
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V. P. Smyshlyaev. The scattering of short waves in a vicinity of a boundary flex point. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 15, Tome 148 (1985), pp. 152-166. http://geodesic.mathdoc.fr/item/ZNSL_1985_148_a15/