Describing and understanding the motion of quantum gases out of
equilibrium is one of the most important modern challenges for
theorists. In the groundbreaking Quantum Newton Cradle experiment
[Kinoshita, Wenger and Weiss, Nature 440, 900
(2006)], quasi-one-dimensional cold atom gases were observed with
unprecedented accuracy, providing impetus for many developments on the
effects of low dimensionality in out-of-equilibrium physics. But it is
only recently that the theory of generalized hydrodynamics has provided
the adequate tools for a numerically efficient description. Using it, we
give a complete numerical study of the time evolution of an ultracold
atomic gas in this setup, in an interacting parameter regime close to
that of the original experiment. We evaluate the full evolving
phase-space distribution of particles. We simulate oscillations due to
the harmonic trap, the collision of clouds without thermalization, and
observe a small elongation of the actual oscillation period and cloud
deformations due to many-body dephasing. We also analyze the effects of
weak anharmonicity. In the experiment, measurements are made after
release from the one-dimensional trap. We evaluate the gas density
curves after such a release, characterizing the actual time necessary
for reaching the asymptotic state where the integrable quasi-particle
momentum distribution function emerges.