Diffraction by a thin cone in the parabolic approximation. method of the boundary integral equation

The problem of diffraction by a thin cone is considered. The parabolic equation of diffraction theory is used as the governing equation. Authors introduce the method of a boundary integral equation for the parabolic equation. The integral equation is derived by applying the Green's theorem. The kernel of the equation has a difference form, so the equation can be solved analytically using Fourier transform. As the result, some known formulae can be re-derived. Also, the integral equation can be solved numerically by iterations.