Fragmented metastable states exist in an attractive Bose-Einstein condensate for atom numbers well above the critical number of the gross-pitaevskii theory

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number NcrGP of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above NcrGP. The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.