Multiple-scale approach for the expansion scaling of superfluid quantum   gases
  We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We discuss how to treat the secular terms appearing in the usual naive expansion in the trap asymmetry parameter epsilon, and calculate the next-to-leading correction for the asymptotic aspect ratio, with significant improvement over the previous proposals. 
I. L. Egusquiza, M. Modugno, M. A. Valle Basagoiti
cond-mat.quant-gas quant-ph