  We discuss the propagation and fractionalization of localized charges on the
edges of quantum Hall bars of variable widths, where interactions between the
edges give rise to Luttinger liquid behavior with a non-trivial interaction
parameter g. We focus in particular on the separation of an initial charge
pulse into a sharply defined front charge and a broader tail. The front pulse
describes an adiabatically dressed electron which carries a non-integer charge,
which is \sqrt{g} times the electron charge. We discuss how the presence of
this fractional charge can, in principle, be detected through measurements of
the noise in the current created by tunneling of electrons into the system. The
results are illustrated by numerical simulations of a simplified model of the
Hall bar.
