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

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