A generalization of the separation of variables method for some 2D diffraction problems

Abstract

A new method is proposed for solving diffraction problems having piecewise linear ideal boundaries. According to this method, the initial Helmholtz equation is replaced by a system of matrix equations of order 1. The coefficients of these equations are rational matrix functions of the coordinates. The properties of the coordinate matrix system are close to that of the ordinary differential equation, therefore the new method can be treated as a generalization of the separation of variables.