  The expansion of a 1D Bose gas is investigated employing the Lieb-Liniger
equation of state within the local density approximation. We show that during
the expansion the density profile of the gas does not follow a self-similar
solution, as one would expect from a simple scaling Ansatz. We carry out a
variational calculation, which recovers the numerical results for the
expansion, the equilibrium properties of the density profile, and the frequency
of the lowest compressional mode. The variational approach allows for the
analysis of the expansion in all interaction regimes between the mean field and
the Tonks-Girardeau limits, and in particular shows the range of parameters for
which the expansion violates self-similarity.
