Interaction of dark solitons with localized impurities in Bose-Einstein condensates

We study the interaction of dark solitons with a localized impurity in Bose-Einstein condensates. We apply the soliton perturbation theory developed earlier in optics for describing the soliton dynamics and soliton-impurity interaction analytically, and then verify the results by direct numerical simulations of the Gross-Pitaevskii equation. We find that a dark soliton can be reflected from or transmitted through a repulsive impurity in a controllable manner, while near the critical point the soliton can be quasitrapped by the impurity. Additionally, we demonstrate that an immobile soliton may be captured and dragged by an adiabatically moving attractive impurity.