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 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.
Publié le : 2009-02-15
Classification:
Waves in random media,
parabolic approximation,
diffusion-approximation,
60H15,
35R60,
74J20
@article{1235140341,
author = {Garnier, Josselin and S\o lna, Knut},
title = {Coupled paraxial wave equations in random media in the white-noise regime},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 318-346},
language = {en},
url = {http://dml.mathdoc.fr/item/1235140341}
}
Garnier, Josselin; Sølna, Knut. Coupled paraxial wave equations in random media in the white-noise regime. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 318-346. http://gdmltest.u-ga.fr/item/1235140341/