Temporal Dark Solitons in Nonuniform Bose-Einstein Condensates
  We discuss temporal dark solitons in confined nonuniform Bose condensates. As a kind of localized high excitation, these solitons can be viewed as macroscopic quasiparticles, having relative motion to the background condensate. We get an analytic expression for one dark soliton under a slowly varying approximation and discuss its special propagation properties in a nonuniform condensate, then we numerically prove that this approximation is reasonable and this kind of soliton exhibits their propagation properties in the nonuniform condensate. Finally, we simulate the generation of dark-soliton-like pulses in the condensate, and indicate that the excitation experiment, done by Ketterle and co-workers [Phys. Rev. Lett. 79, 553 (1997)], can also be interpreted in terms of temporal dark soliton. 
Tao Hong, Yu Zhu Wang and Yun Sheng Huo