  We investigate the propagation of density-wave packets in a Bose-Hubbard
model using the adaptive time-dependent density-matrix renormalization group
method. We discuss the decay of the amplitude with time and the dependence of
the velocity on density, interaction strength and the height of the
perturbation in a numerically exact way, covering arbitrary interactions and
amplitudes of the perturbation. In addition, we investigate the effect of
self-steepening due to the amplitude dependence of the velocity and discuss the
possibilities for an experimental detection of the moving wave packet in time
of flight pictures. By comparing the sound velocity to theoretical predictions,
we determine the limits of a Gross-Pitaevskii or Bogoliubov type description
and the regime where repulsive one-dimensional Bose gases exhibit fermionic
behaviour.
