Dynamic Properties Of Solitons In One-Dimensional Bose-Einstein Condensate

In this thesis, we investigate Bose-Einstein condensate and the properties of solitons in BEC by the numerical simulation based on Gross-Pitaevskii equation. The dynamics of dark solitons for one-dimensional BEC in an expulsive parabolic potential is discussed in detail. The result is different from the dynamics of solitons in optical propagation. It is meaningful for us to understand the dynamics of microphysical field. The main contents are as follow:(1) The concept of BEC and its main characters are given. The vital experimental technology of production BEC-cooling and trapping, absorbing image are demonstrated. The development of the experimental research work on BEC is summarized.(2) The conditions of formation are discussed. At the mean-field level, the NLS equation is derived from both Heisenberg equation and the variation procedure. Furthermore, the formation of solitons in BEC is explained.(3) The dynamics of dark soliton for one-dimensional BEC in an expulsive parabolic potential is analyzed in detail. The motion of a dark soliton is investigated. Furthermore, the dynamics of dark soliton and the interaction between two dark solitons are discussed in detail by numerical simulation. The result shows that the motion of dark soliton is periodical, and the interaction between two dark solitons exhibits to collide each other periodically. As the separation between two dark solitons becomes shorter, the periodical colliding is shrinking and the period of the colliding action is shorter.