Collective excitations of a Bose-Einstein condensate in an anharmonic   trap
  We investigate the collective excitations of a one-dimensional Bose-Einstein condensate (BEC) with repulsive interaction between atoms in a quadratic plus quartic trap. By using the variational approach, the coupled equations of motion for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations, which originate from the nonlinear coupling between the two modes, are discussed. 
Guan-Qiang Li, Li-Bin Fu, Ju-Kui Xue, Xu-Zong Chen, and Jie Liu