Beyond the Thomas-Fermi Approximation for Nonlinear Dynamics of Trapped Bose-Condensed Gases

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We present an analytical approximation for nonlinear dynamics of trapped Bose-co ndensed gases. The new approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms $N$. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments.
10 pages, 1 figure, 3 tables

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