Diffraction by a narrow cone at skew incidence

The scalar problem of plane wave diffraction by a narrow cone is considered. The angle of the cone $\alpha$ and the angle of incidence are assumed to be small and the field is studied in a boundary layer near the surface at such distances $z$ from the cone tip that $kz\sim\alpha^{-2}$. The parabolic equation method is applied and the leading order approximation is constructed in the form of an integral.