  We analyze motion of a fluxon in a weakly damped ac-driven long Josephson
junction with a periodically modulated maximum Josephson current density. We
demonstrate both analytically and numerically that a pure {\it ac} bias current
can drive the fluxon at a {\it resonant} mean velocity determined by the
driving frequency and the spatial period of the modulation, provided that the
drive amplitude exceeds a certain threshold value. In the range of strongly
``relativistic'' mean velocities, the agreement between results of a numerical
solution of the effective (ODE) fluxon equation of motion and analytical
results obtained by means of the harmonic-balance analysis is fairly good;
morever, a preliminary PDE result tends to confirm the validity of the
collective-coordinate (PDE-ODE) reduction. At nonrelativistic mean velocities,
the basin of attraction, in position-velocity space, for phase-locked solutions
becomes progressively smaller as the mean velocity is decreased.
