Singularity formation in the Gross-Pitaevskii Equation and Collapse in   BEC
  We study a mechanism of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for the particle flux and introduce a collapsing fraction of particles. We assume that the collapsing fraction is expelled from the condensate due to dissipation. Using this hypothesis we analyze the dependence of the condensate collapse on the initial conditions. We found that for a properly chosen negative scattering length the remnant fraction becomes larger when the initial aspect ratio is increased. 
A.V. Rybin, I.P. Vadeiko, G.G. Varzugin, J. Timonen