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Fast soliton scattering by delta impurities
PDE Seminar| Speaker: | Maciej Zworski, University of California at Berkeley |
| Location: | 3106 MSB |
| Start time: | Thu, May 4 2006, 3:10PM |
Description
We study the Gross-Pitaevskii equation (nonlinear Schroedinger equation)
with a repulsive delta function potential. We show that a high velocity
incoming soliton is split into a transmitted component and a reflected
component. The transmitted mass (L^2 norm squared) is shown to be in good
agreement with the quantum transmission rate of the delta function
potential. We further show that the transmitted and reflected components
resolve into solitons plus dispersive radiation, and quantify the mass and
phase of these solitons.