ИСТИНА

The problem of diffraction by a body having a rotational symmetry is studied (examples of such problems are diffraction by a cone or diffraction by a junction of several cones). The incidence is assumed to be axial. The problem is considered in the parabolic approximation from the very beginning, i.e. the governing equation for the waves is the parabolic equation of diffraction theory. The boundary conditions are of Neumann type . The problem is solved using the boundary integral equation of the Hong's type . Such an equation is derived in the Cartesian coordinates. This equation is of the Volterra type, so it can be solved by iterations. Besides, in the general case the equation can be solved numerically and for some particular cases (e.g. for diffraction by a cone) it can be solved analytically. In the talk we demonstrate the capabilities of the boundary integral equation method in the parabolic approximation. Some known formulae are re-derived using this method. Numerical results are presented.