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We give numerical estimates of various unstable stationary solutions of theGross--Pitaevskii equation in an axially symmetric set up with a lineartrapping potential along the symmetry axis, and a quadratic trapping along theradial direction. These represent topological coherent modes of Bose--Einsteincondensates in a gravito optical surface trap (GOST). Despite theirinstability, we find that many of these solutions decay sufficiently slow, sothat they could be realized experimentally.

Life time of topological coherent modes of a Bose--Einstein condensate in a gravito optical surface trap