Stability of Solution of the Nonlinear Schr\"odinger Equation for the Bose-Einstein Condensation
Abstract
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 Ncr of atoms for a metastable state to exist. Our calculated value of Ncr 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.
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