  We propose a versatile variational method to investigate the spatio-temporal
dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this
end we employ a \emph{q}-Gaussian trial wave-function that interpolates between
the low- and the high-density limit of the ground state of a Bose-condensed
gas. Our main result consists of reducing the Gross-Pitaevskii equation, a
nonlinear partial differential equation describing the T=0 dynamics of the
condensate, to a set of only three equations: \emph{two coupled nonlinear
ordinary differential equations} describing the phase and the curvature of the
wave-function and \emph{a separate algebraic equation} yielding the generalized
width. Our equations recover those of the usual Gaussian variational approach
(in the low-density regime), and the hydrodynamic equations that describe the
high-density regime. Finally, we show a detailed comparison between the
numerical results of our equations and those of the original Gross-Pitaevskii
equation.
