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. 
Dmitry A. Zezyulin, Georgy L. Alfimov, Vladimir V. Konotop, Victor M.   Perez-Garcia