Bright and dark solitons in a Bose-Einstein condensate

Abstract

We study dark and bright solitons in confined Bose-Einstein condensates of ultracold gases with repulsive and attractive atom-atom interaction. First, we compute analytic properties of the solitons in absence of the trap. Then, we consider the problem of the collision of a bright soliton with a barrier. This is studied by solving numerically the 1D Gross-Pitaevskii equation in the presence of a harmonic oscillator potential and a Rosen-Morse barrier. We discuss in detail the conditions for having a transmission coefficient of T = 0:5. Then, we study the evolution of the energies during this process and the nature of the part transmitted