Josephson Dynamics of a Bose--Einstein Condensate Trapped in a Double-Well Potential

The Josephson equations for a Bose--Einstein Condensate gas trapped in a
double-well potential are derived with the two-mode approximation by the
Gross--Pitaevskii equation. The dynamical characteristics of the equations are obtained by the numerical phase diagrams. The nonlinear self-trapping effect appeared in the phase diagrams are emphatically discussed, and the condition E_cN>4E_J is presented.