Stability of Solution of the Nonlinear Schr\"odinger Equation for the   Bose-Einstein Condensation
  We investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for determining the upper bound of the critical numbers $N_{cr}$ of atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for Bose-Einstein condensation of lithium atoms based on our new equation is in agreement with those observed in a agreement with those observed in a recent experiment. 
Yeong E. Kim and Alexander L. Zubarev (Department of Physics, Purdue   University)