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Self-averaging in time reversal for the parabolic wave equation. (English) Zbl 1020.35126
The aim of this paper is to examine time reversal in the radiative transfer regime using the parabolic wave equation, when the waves interact fully with the random inhomogeneities. The authors prove mathematically that the refocused signal is self-averaging, which means that it does not depend on the realization of the random medium. The mathematical quantity that the authors analyze is the Wigner measure of a pair of oscillatory solutions of the random Schrödinger equation.

MSC:
35R60 PDEs with randomness, stochastic partial differential equations
35Q40 PDEs in connection with quantum mechanics
60H25 Random operators and equations (aspects of stochastic analysis)
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