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.
Copyright (2009) by the American Physical Society. DOI: 10.1103/PhysRevE.75.036601
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