Stability of excited states of a Bose-Einstein condensate in an anharmonic trap

We analyze the stability of non-ground nonlinear states of a Bose-Einstein condensate in the mean field limit in effectively 1D (``cigar-shape'') traps for various types of confining potentials. We find that nonlinear states become, in general, more stable when switching from a harmonic potential to an anharmonic one. We discuss the relation between this fact and the specifics of the harmonic potential which has an equidistant spectrum.