Green’s Function of Wave Equation for Inhomogeneous Medium

Abstract

A method is proposed for constructing the Green’s function for the wave equation describing wave propagation in the ionosphere with electronic density N(z,x) depending on two independent variables. By means of the Fourier transform with respect to t, we obtain a reduced wave equation with an inhomo-geneous term of the δ-function type. The last problem solution has the form of integral containing the eigenfunctions of one-dimensional problem. The eigenfunctions depend on the parameter x. The expansion coefficients satisfy the second kind integral equation. In the weak dependence case of electronic density on a coordinate x, the integral equation can be solved by the successive approximations method.