  In this paper we study nonequilibrium dynamics of one dimensional Bose gas
from the general perspective of dynamics of integrable systems. After outlining
and critically reviewing methods based on inverse scattering transform,
intertwining operators, q-deformed objects, and extended dynamical conformal
symmetry, we focus on the form-factor based approach. Motivated by possible
applications in nonlinear quantum optics and experiments with ultracold atoms,
we concentrate on the regime of strong repulsive interactions. We consider
dynamical evolution starting from two initial states: a condensate of particles
in a state with zero momentum and a condensate of particles in a gaussian
wavepacket in real space. Combining the form-factor approach with the method of
intertwining operator we develop a numerical procedure which allows explicit
summation over intermediate states and analysis of the time evolution of
non-local density-density correlation functions. In both cases we observe a
tendency toward formation of crystal-like correlations at intermediate time
scales.
