  Dynamics of a fluxon in a stack of inductively coupled long Josephson
junctions is studied analytically and numerically. We demonstrate that the
fluxon has a maximum velocity, which does not necessarily coincide with any of
the characteristic Josephson plasma wave velocities. The maximum fluxon
velocity is found by means of numerical simulations of the quasi-infinite
system. Using the variational approximation, we propose a simple analytical
formula for the dependence of the fluxon's maximum velocity on the coupling
constant and on the distribution of critical currents in different layers. This
analysis yields rather precise results in the limit of small dissipation. The
simulations also show that nonzero dissipation additionally stabilizes the
fluxon.
