Remarks on the Parabolic Equation Model for Waves in Random Media

One of the most important contributions of V.I. Tatarskii is the introduction and development of the parabolic equation model (PEM) for waves in random media (WRM). Most of the theories for WRM are based on perturbation methods that place stringent constraints on the magnitude of refractive index fluctuations. The PEM was hence introduced as a strong fluctuation theory. An important merit of the theory is that one can obtain closed equations for moments of wave functions of any order. This model is based on the following three assumptions: (a) wave propagation is predominant in one direction (negligible backscatter), (b) the refractive index fluctuations obey Gaussian statistics, and (c) the random medium is delta correlated along the direction of propagation. In spite of the restrictions imposed by these assumptions, PEM has been quite successful in numerous applications since 1970.