  We study a quench protocol where the ground state of a free many-particle
bosonic theory in one dimension is let unitarily evolve in time under the
integrable Lieb-Liniger Hamiltonian of $\delta$-interacting repulsive bosons.
By using a recently-proposed variational method, we here obtain the exact
non-thermal steady-state of the system in the thermodynamic limit, and discuss
some of its main physical properties. Besides being a rare case of a
thermodynamically exact solution to a truly interacting quench situation, this
interestingly represents an example where a naive implementation of the
generalized Gibbs ensemble fails.
