Coupled Paraxial Wave Equations in Random Media in the White-noise Regime

In this paper the reflection and transmission of waves by a threedimensional random medium is studied in a high-frequency, whitenoise, and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schrödinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation functions are determined by a closed system of transport equations. The Wigner distribution is then used to describe the enhanced backscattering phenomenon for the reflected field.