Approximation for nonlinear dynamics of trapped Bose-Einstein condensates

We present an analytical approximation for nonlinear dynamics of trapped Bose-Einstein condensates. The 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. The approximation is useful in providing a simple and easy quantitative computational tool for the analysis of experimental data