We investigate the collective excitations of an one-dimensional Bose-Einstein condensate with repulsive interaction between atoms in a quadratic plus quartic trap. With using variational approaches, the coupled equations of motions 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 originated from the nonlinear coupling between the two modes, are discussed.

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