The Annals of Applied Probability

Coupled paraxial wave equations in random media in the white-noise regime

Josselin Garnier and Knut Sølna

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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.

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Ann. Appl. Probab., Volume 19, Number 1 (2009), 318-346.

First available in Project Euclid: 20 February 2009

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Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 74J20: Wave scattering

Waves in random media parabolic approximation diffusion-approximation


Garnier, Josselin; Sølna, Knut. Coupled paraxial wave equations in random media in the white-noise regime. Ann. Appl. Probab. 19 (2009), no. 1, 318--346. doi:10.1214/08-AAP543.

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