Violation of self-similarity in the expansion of a 1D Bose gas

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.