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Some examples on solution structures for weakly nonlinear elliptic equations
Stability of time reversed waves in changing media
1.  Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027, United States 
2.  Department of Mathematics, University of Chicago, Chicago IL, 60637, United States 
The refocusing quality of the backpropagated signal is determined by the cross correlation of the two media. When the two media decorrelate, two distinct defocusing effects are observed. The first one is a purely absorbing effect due to the loss of coherence at a fixed frequency. The second one is a phase modulation effect of the refocused signal at each frequency. This causes defocusing of the backpropagated signal in the time domain.
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