2013 / December Volume 8 No.4
Long-Time Behavior of the Schrodinger-Langevin Equation
| Published Date |
2013 / December
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|---|---|
| Title | Long-Time Behavior of the Schrodinger-Langevin Equation |
| Author | |
| Keyword | |
| Download | |
| Pagination | 505-544 |
| Abstract | We consider the large time behavior for
nonlinear Schr\"odinger--Langevin equation in one dimension for WKB-initial data with different density at left/right far fields. We
show that the momentum damping overwhelms the quantum dispersion. Thus, unlike those in scattering theory, the solution tends
to an asymptotic state determined by a porous media equation. More precisely, the total density tends pointwise to a nonlinear diffusion wave and the phase tends to a corresponding function.
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| AMS Subject Classification |
35B40, 35Q53
|
| Received |
2013-08-31
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| Accepted |
2013-08-31
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