Dark soliton in the Bose–Einstein condensates with nonlinearity and harmonic potential managements

The dynamics of dark solitons in one-dimensional Bose–Einstein condensates under the nonlinearity and harmonic potential managements is investigated. It is found that at the large particle limit the macroscopic wave function could evolve self-similarly, which provides a time-varying background for the propagation of dark solitons. The approximate dark soliton solution is derived and its center-of-mass motion is predicted analytically.