Nonlinear Schrr Odinger Solitons Scattering Oo an Interface

We integrate the one-dimensional nonlinear Schrr odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering oo an interface separating two regions of constant potential modeled by a linear ramp. Transmission coeecients and inelasticities are computed as functions of the potential diierence and the slope of the ramp. Our data show that the ramp's slope has a strong innuence revealing unexpected windows of reeection in a transmission regime. The transmission coeecients for very small potential diierences 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 ampliied amplitude. Due to this, they oscillate. The oscillation period is measured and compared with theoretical predictions.