Radiation from a convex equi-phase surface: Malyuzhinets' parabolic equation

In this work we study the possibility of applying Malyuzhinets' parabolic equation to the problem of acoustical or electromagnetic wave radiation by a curved conformal antenna. In order to obtain an explicit analytical solution we consider a simplified 2D problem: harmonic wave field produced by equi-phase excitation of a convex body surface. The excitation amplitude may vary slowly from point to point, resulting in diffraction effects that determine the far-field radiation pattern.