New approach to the wave diffraction by arbitrary dielectric wedge

The problem of diffraction of an E-polarized plane wave by a dielectric wedge has been treated by a number of authors. In this paper, the integral representations are used for inside and outside solutions. The boundary conditions lead to coupled integral equations of the first kind. In any case, the solution of the integral equation of the 1-st kind leads to an ill-conditioned algebraic system. As a rule, the solution of such a system is connected with any ill-posed problem. The integral transformation is found for the system of integral equations of the 1-st kind and this transformation enables one to obtain a stable solution