Boundary integral equation method for the parabolic equation on the curved surface

A 2D problem of diffraction by a curved surface with Neumann boundary conditions is considered. The incident wave is assumed to fall almost tangentially to the surface. The problem is studied in the parabolic approximation. A boundary integral equation of Hong's type is derived for the field. This equation belongs to Volterra class. A test problem of diffraction by a parabola is solved. An analytical solution of the integral equation can be found, and this solution is similar to well-known solution by V. A. Fock. A numerical solution of the equation is obtained by iterations.