  We study the behavior of excitations in the tilted one-dimensional
Bose-Hubbard model. In the phase with broken symmetry, fundamental excitations
are domain-walls which show fractional statistics. Using perturbation theory,
we derive an analytic model for the time evolution of these fractional
excitations, and demonstrate the existence of a repulsively bound state above a
critical center of mass momentum. The validity of the perturbative analysis is
confirmed by the use of t- DMRG simulations. These findings open the path for
experimental detection of fractional particles in cold atomic gases.
