A trajectory approach is taken to the hydrodynamical treatment of collective excitations of a Bose-Einstein condensate in a harmonic trap. The excitations induced by linear deformations of the trap are shown to constitute a broad class of solutions that can be fully described by a simple nonlinear matrix equation. An exact closed-form expression is obtained for the solution describing the mode n=0, m=+2 in a cylindrically symmetric trap, and the calculated amplitude-dependent frequency shift shows good agreement with the experimental results of the JILA group.
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Storey et al. (2000) studied this question.
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