  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.
