 Previous Article
 DCDS Home
 This Issue

Next Article
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.
[1] 
Stephen Coombes, Helmut Schmidt, Carlo R. Laing, Nils Svanstedt, John A. Wyller. Waves in random neural media. Discrete & Continuous Dynamical Systems  A, 2012, 32 (8) : 29512970. doi: 10.3934/dcds.2012.32.2951 
[2] 
Rémi Carles, Clotilde FermanianKammerer, Norbert J. Mauser, Hans Peter Stimming. On the time evolution of Wigner measures for Schrödinger equations. Communications on Pure & Applied Analysis, 2009, 8 (2) : 559585. doi: 10.3934/cpaa.2009.8.559 
[3] 
Albert Fannjiang, Knut Solna. Time reversal of parabolic waves and twofrequency Wigner distribution. Discrete & Continuous Dynamical Systems  B, 2006, 6 (4) : 783802. doi: 10.3934/dcdsb.2006.6.783 
[4] 
TzongYow Lee and Fred Torcaso. Wave propagation in a lattice KPP equation in random media. Electronic Research Announcements, 1997, 3: 121125. 
[5] 
Guillaume Bal, Olivier Pinaud. Selfaveraging of kinetic models for waves in random media. Kinetic & Related Models, 2008, 1 (1) : 85100. doi: 10.3934/krm.2008.1.85 
[6] 
Guillaume Bal. Homogenization in random media and effective medium theory for high frequency waves. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 473492. doi: 10.3934/dcdsb.2007.8.473 
[7] 
Thierry Colin, Pierre Fabrie. Semidiscretization in time for nonlinear Schrödingerwaves equations. Discrete & Continuous Dynamical Systems  A, 1998, 4 (4) : 671690. doi: 10.3934/dcds.1998.4.671 
[8] 
Wolfgang Wagner. A random cloud model for the Wigner equation. Kinetic & Related Models, 2016, 9 (1) : 217235. doi: 10.3934/krm.2016.9.217 
[9] 
Zhengping Wang, HuanSong Zhou. Radial signchanging solution for fractional Schrödinger equation. Discrete & Continuous Dynamical Systems  A, 2016, 36 (1) : 499508. doi: 10.3934/dcds.2016.36.499 
[10] 
Addolorata Salvatore. Signchanging solutions for an asymptotically linear Schrödinger equation. Conference Publications, 2009, 2009 (Special) : 669677. doi: 10.3934/proc.2009.2009.669 
[11] 
Feng Cao, Wenxian Shen. Spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media. Discrete & Continuous Dynamical Systems  A, 2017, 37 (9) : 46974727. doi: 10.3934/dcds.2017202 
[12] 
Wenxian Shen, Zhongwei Shen. Transition fronts in nonlocal FisherKPP equations in time heterogeneous media. Communications on Pure & Applied Analysis, 2016, 15 (4) : 11931213. doi: 10.3934/cpaa.2016.15.1193 
[13] 
Mattia Turra. Existence and extinction in finite time for Stratonovich gradient noise porous media equations. Evolution Equations & Control Theory, 2019, 8 (4) : 867882. doi: 10.3934/eect.2019042 
[14] 
Wolfgang Wagner. A random cloud model for the Schrödinger equation. Kinetic & Related Models, 2014, 7 (2) : 361379. doi: 10.3934/krm.2014.7.361 
[15] 
Norbert Požár, Giang Thi Thu Vu. Longtime behavior of the onephase Stefan problem in periodic and random media. Discrete & Continuous Dynamical Systems  S, 2018, 11 (5) : 9911010. doi: 10.3934/dcdss.2018058 
[16] 
Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems  A, 2010, 28 (4) : 13111343. doi: 10.3934/dcds.2010.28.1311 
[17] 
Tomáš Roubíček. An energyconserving timediscretisation scheme for poroelastic media with phasefield fracture emitting waves and heat. Discrete & Continuous Dynamical Systems  S, 2017, 10 (4) : 867893. doi: 10.3934/dcdss.2017044 
[18] 
Josselin Garnier. Ghost imaging in the random paraxial regime. Inverse Problems & Imaging, 2016, 10 (2) : 409432. doi: 10.3934/ipi.2016006 
[19] 
Grégoire Allaire, M. Vanninathan. Homogenization of the Schrödinger equation with a time oscillating potential. Discrete & Continuous Dynamical Systems  B, 2006, 6 (1) : 116. doi: 10.3934/dcdsb.2006.6.1 
[20] 
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete & Continuous Dynamical Systems  A, 2016, 36 (12) : 69436974. doi: 10.3934/dcds.2016102 
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]