results have direct implications for the atom laser and the Josephson effect for atoms. Recently, solitons have been generated in BEC by properly phase imprinting \[5\], the phase of a BEC wave-function was prepared with optical imprinting techniques and measured with a Mach-Zehnder matter-wave interferometer that makes use of optically induced Bragg diffraction.

Experimental achievements of BEC caused great theoretical interests in this novel field. There exists abundant nonlinear dynamics in BEC, for the macroscopic condensate wave function obeys a nonlinear equation, which is called as the Gross-Pitaveskii equation (GPE) \[6\]. Vortex stability in BEC is explained by using a two-mode model \[7\]. Oscillations of atomic populations and collective excitations at high energies was detailed \[8\], the complex dependencies of these excitation energies bring us close to the notion of chaos, and the role of chaotic motions in the dynamics of BEC remains to be studied. Large amplitude oscillations of condensed trapped atoms to external driving magnetic fields was analyzed by the group of Smerzi \[9\], their results of frequencies and excitation times of collective oscillations consistent with the experimental data very much. An appropriate semiclassical limit for GPE with an additional chaotic potential was given out by using a 