  We scrutinize the hydrodynamic approach for calculating dynamical
correlations in one-dimensional superfluids near integrability and calculate
the characteristic time scale {\tau} beyond which this approach is valid. For
time scales shorter than {\tau} hydrodynamics fails and we develop an approach
based on kinetics of fermionic quasiparticles described as mobile impurities.
New universal results for the dynamical structure factor relevant to
experiments in ultracold atomic gases are obtained.
