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We find that the key features of the evolution and collapse of a trapped Bosecondensate with negative scattering length are predetermined by the particleflux from the above-condensate cloud to the condensate and by 3-bodyrecombination of Bose-condensed atoms. The collapse, starting once the numberof Bose-condensed atoms reaches the critical value, ceases and turns toexpansion when the density of the collapsing cloud becomes so high that therecombination losses dominate over attractive interparticle interaction. As aresult, we obtain a sequence of collapses, each of them followed by dynamicoscillations of the condensate. In every collapse the 3-body recombinationburns only a part of the condensate, and the number of Bose-condensed atomsalways remains finite. However, it can comparatively slowly decrease after thecollapse, due to the transfer of the condensate particles to theabove-condensate cloud in the course of damping of the condensate oscillations.Comment: 11 pages, 3 figure

Collapse and Bose-Einstein Condensation in a Trapped Bose Gas with Negative Scattering Length