  In recent years there has been an intensive search for Majorana fermion
states in condensed matter systems. Predicted to be localized on cores of
vortices in certain non-conventional superconductors, their presence is known
to render the exchange statistics of bulk vortices non-Abelian. Here we study
the equations governing the dynamics of phase solitons (fluxons) in a long
Josephson junction in a topological superconductor. We show that the fluxon
will bind a localized zero energy Majorana mode and will consequently behave as
a non-Abelian anyon. The low mass of the fluxon, as well as its experimentally
observed quantum mechanical wave-like nature, will make it a suitable candidate
for vortex interferometry experiments demonstrating non-Abelian statistics. We
suggest two experiments that may reveal the presence of the zero mode carried
by the fluxon. Specific experimental realizations will be discussed as well.
