Method of generalized eikonal and new 2-D scattering analytical solutions

A method for analytical solving of 2-D diffraction problems was introduced in previous studies. In this paper, the main features of the final version of the method are formulated. The purpose of the method is to solve 2-D Helmholtz equation boundary value problem for perfectly conducting scatterers of arbitrary shape. The key point of the method lies in the usage of integral representations received for special generalized "eikonal function" satisfying Laplace equation in one region (supplementary region) as a solution in another region (main region) of the boundary value problem for the Helmholtz equation with a variable wavenumber.