Stability of the trapped nonconservative Gross-Pitaevskii equation with   attractive two-body interaction
  The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments. 
Victo S. Filho, T. Frederico, Arnaldo Gammal, and Lauro Tomio