Fast soliton scattering by delta impurities
  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. 
Justin Holmer, Jeremy Marzuola, Maciej Zworski