Name
Abstract | ||
|---|---|---|
We consider the random Schrodinger equation as it arises in the paraxial regime for wave propagation in random media. In the white noise limit it becomes the Ito-Schrodinger stochastic partial di. erential equation which we analyze here in the high frequency regime. We also consider the large lateral diversity limit where the typical width of the propagating beam is large compared to the correlation length of the random medium. We use the Wigner transform of the wave. eld and show that it becomes deterministic in the large diversity limit when integrated against test functions. This is the self- averaging property of the Wigner transform. It follows easily when the support of the test functions is of the order of the beam width. We also show with a more detailed analysis that the limit is deterministic when the support of the test functions tends to zero but is large compared to the correlation length. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/060668882 | MULTISCALE MODELING & SIMULATION |
Keywords | Field | DocType |
random media,parabolic approximation,stochastic partial differential equations | Parabolic partial differential equation,Mathematical optimization,Mathematical analysis,Schrödinger equation,Self-averaging,Correlation function (statistical mechanics),First-order partial differential equation,Stochastic differential equation,White noise,Stochastic partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
6 | 2 | 1540-3459 |
Citations | PageRank | References |
3 | 0.60 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| George Papanicolaou | 1 | 199 | 50.21 |
| Lenya Ryzhik | 2 | 4 | 3.06 |
| Knut Sølna | 3 | 142 | 46.02 |