Nonlinear Schr\"odinger solitons scattering off an interface
  We integrate the one-dimensional nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an interface separating two regions of constant potential modeled by a linear ramp. Transmission coefficients and inelasticities are computed as functions of the potential difference and the slope of the ramp. Our data show that the ramp's slope has a strong influence revealing unexpected windows of reflection in a transmission regime. The transmission coefficients for very small potential differences are compared with the theoretical predictions derived by perturbation theory. Also the time evolution of the solitary waves after the scattering is studied. We observed that they in general behave like solitons with an amplified amplitude. Due to this, they oscillate. The oscillation period is measured and compared with theoretical predictions.   PACS number(s): 03.40.Kf, 0.3.65.Ge, 42.65.Tg, 42.81.Dp 
H. Frauenkron (HLRZ c/o Forschungszentrum J\"ulich GmbH, J\"ulich,   Germany)