Finite difference method for research of wave beam propagation in nonlinear inhomogeneous lossy media

This work originates from the need to construct an automatic solution for the problems of Gaussian beam (GB) propagation in various media and scattering on arbitrary smooth bodies. The solution is obtained using a finite difference (FD) technique applied to the complex eikonal equation and (optionally) to the transport equations. The authors consider the ray-tracing technique, which is very simple and easily realizable numerically. The eikonal equation has been solved using complex rays tracing. Numerical solution of the eikonal equation allows the dependence of the refraction coefficient on the coordinates and the amplitude to be taken into account easily.