COUPLED PARAXIAL WAVE EQUATIONS IN RANDOM MEDIA IN THE WHITE-NOISE REGIME

• 成果类型: Article
• 署名作者: Garnier, Josselin; Solna, Knut
• 署名单位: Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; University of California System; University of California Irvine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP543
• 发表日期: 2009
• 页码: 318-346
• 关键词: transport-equations; time-reversal; approximation; propagation; backscattering; beam

摘要

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 Schrodinger 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.