  Using a numerical renormalization group based on exploiting an underlying
exactly solvable non- relativistic theory, we study the out-of-equilibrium
dynamics of a 1D Bose gas (as described by the Lieb-Liniger model) released
from a parabolic trap. Our method allows us to track the post-quench dynamics
of the gas all the way to infinite time. We also exhibit a general
construction, applicable to all integrable models, of the thermodynamic
ensemble that has been suggested to govern this dynamics, the generalized Gibbs
ensemble. We compare the predictions of equilibration from this ensemble
against the long time dynamics observed using our method.
