ИСТИНА

The method of parabolic equation is used in diffraction theory to describe waves having a narrow angular spectrum. Namely, the parabolic approximation can be applied to the wide range of problems: the problem of diffraction by a strip, by a body of revolution, and to some waveguide problems. Some of these problems can be solved explicitly in the parabolic approximation. Moreover, numerous numerical experiments show that the parabolic approximation works well even in the case when the diffraction process cannot be treated as paraxial. In the current work authors try to understand why it works better then expected. The problem of diffraction by a half-plane is considered. First, a problem for the parabolic equation with appropriate boundary conditions is introduced. Second, the problem is reduced to the boundary integral equation. The same procedure is repeated for the initial (Helmholtz) problem and the Wiener-Hopf equation is derived. It is found out that the kernel of the ``parabolic'' equation is one of the factors of the factorization of the ``Helmholtz'' equation kernel. This fact explains why the parabolic equation works well for the half-plane problem (even near the edge of the half-plane). Possible generalizations of this result is discussed. The work is supported by the RSF grant 14-22-00042.