We develop an algorithm using two coupled parabolic equations for numerical simulation of wave propagation over long distances. The coupled parabolic equations are derived from a two mode wave decomposition. An iterative procedure is used in our numerical algorithm. The coupling between the two parabolic equations allow us to deal with fine scale inhomogeneities in the medium and capture the back scattering that are usually neglected in a one way parabolic approximation. We study stability issues of our numerical algorithm and present numerical examples.
"Coupled Parabolic Equations for Wave Propagation." Methods Appl. Anal. 11 (3) 399 - 412, September 2004.