%0 Journal Article
%T Coupled paraxial wave equations in random media in the white-noise regime
%A Josselin Garnier
%A Knut S£¿lna
%J Mathematics
%D 2009
%I arXiv
%R 10.1214/08-AAP543
%X In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schr\"{o}dinger 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.
%U http://arxiv.org/abs/0903.0449v1