The scattering of short waves in a vicinity of a boundary flex point

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.