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The dynamics of a nonconservative Gross-Pitaevskii equation for trappedatomic systems with attractive two-body interaction is numericallyinvestigated, considering wide variations of the nonconservative parameters,related to atomic feeding and dissipation. We study the possible limitations ofthe mean field description for an atomic condensate with attractive two-bodyinteraction, by defining the parameter regions where stable or unstableformation can be found. The present study is useful and timely considering thepossibility of large variations of attractive two-body scattering lengths,which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction