Collapse And Global Stability Of Attractive Bose-Einstein Condensation

This paper deals with the Gross-Pitaevskii(GP) equation which is used to describe attractive Bose-Einstein condensation and the equation is also called nonlinear Schr?dinger equation with harmonic potential.In charpter 2,the GP equation without damped term is studied as following form =, where a,b are constant parameters,1firstly the collapse of the equation is obtained by developing the means of M.Tsutsumi,subsequently the global stability of the equation is obtained by referring to relative ideas of M.I.Weinstein and Jian Zhang.