  A novel dynamical effect is presented: systematic drift of a topological
soliton in ac-driven weakly damped systems with periodic boundary conditions.
The effect is demonstrated in detail for a long annular Josephson junction.
Unlike earlier considered cases of the ac-driven motion of fluxons (kinks), in
the present case the long junction is_spatially uniform_. Numerical simulations
reveal that progressive motion of the fluxon commences if the amplitude of the
ac drive exceeds a threshold value. The direction of the motion is randomly
selected by initial conditions, and a strong hysteresis is observed. An
analytical approach to the problem is based on consideration of the interaction
between plasma waves emitted by the fluxon under the action of the ac drive and
the fluxon itself, after the waves complete round trip in the annular junction.
The analysis predicts instability of the zero-average-velocity state of the
fluxon interacting with its own radiation tails, provided that the drive's
amplitude exceeds an explicitly found threshold. The predicted threshold
amplitude strongly depends on the phase shift gained by the wave after the
round trip. A very similar dependence is found in the simulations, testifying
to the relevance of the analytical consideration.
