We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers.
van Wijk, Kasper. (2007). "Modified Kubelka-Munk Equations for Localized Waves Inside a Layered Medium". Physical Review E, 75(3), 036601-1 - 036601-8. http://dx.doi.org/10.1103/PhysRevE.75.036601