Effect of a localized impurity on soliton dynamics in the Bose–Einstein condensates

By using a multiple-scale method, we analytically study the effect of a localized impurity on the soliton dynamics in the Bose–Einstein condensates. It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity, while at the position of the localized impurity the soliton can be quasitrapped by the impurity. Additionally, we find that the strength of the localized impurity has an important effect on the dark soliton dynamics. With increasing strength of the localized impurity, the amplitude of the dark soliton becomes bigger, while its width is narrower, and the soliton propagates slower.