Mathematics – Analysis of PDEs
Scientific paper
2006-02-09
Mathematics
Analysis of PDEs
32 pages, 3 figures
Scientific paper
10.1007/s00220-007-0261-z
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.
Holmer Justin
Marzuola Jeremy
Zworski Maciej
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