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.
