Dynamics of the Bose-Einstein condensate: quasi-one-dimension and beyond

It is shown that the quasi-one-dimensional Bose-Einstein condensate is expe rimentally accessible and rich in intriguing phenomena. We demonstrate nume rically and analytically the existence, stability and perturbation-induced dynamics of all types of stationary states of the quasi-one-dimensional non linear Schrodinger equation for both repulsive and attractive cases. Among our results are: the connection between stationary states and solitons; cre ation of vortices from such states; manipulation of such states with simple phase profiles; demonstration of the fragility of the condensate phase in response to shock; and a robust stabilization of the attractive Bose-Einste in condensate.