High frequency approximation of the Green´s function of the Helmholtz´s equation for inhomogeneous medium

A method is proposed for constructing the Green´s function for the reduced wave equation describing wave propagation in the ionosphere with electronic density N(z, x) depending on two independent variables. This problem solution has the form of an integral containing the eigenfunctions of a 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 the electronic density on a coordinate x and in the case when the asymptotic parameter K_o is great enough, the integral equation can be solved by the successive approximations method