Parametric Quantum Resonances for Bose-Einstein Condensates
  We generalize recent work on parametric resonances for nonlinear Schr{\"o}dinger (NLS) type equations to the case of three dimensional Bose-Einstein condensates at zero temperatures. We show the possibility of such resonances in the three-dimensional case, using a moment method and numerical simulations. 
P. G. Kevrekidis, A. R. Bishop, and K.{\O}. Rasmussen