Avoiding Infrared Catastrophes in Trapped Bose-Einstein Condensates
  This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in ``cigar-shaped'' (1D) attractive BECs and the transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to ``engineer'' the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior. 
P.G. Kevrekidis (1), G. Theocharis (2), D.J. Frantzeskakis (2), and A.   Trombettoni (3) ((1) Department of Mathematics and ...