  The dynamical behavior of a harmonic chain in a spatially periodic potential
(Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of
an external force and a velocity proportional damping is investigated. We do
this at zero temperature for long chains in a regime where inertia and damping
as well as the nearest-neighbor interaction and the potential are of the same
order. There are two types of regular sliding states: Uniform sliding states,
which are periodic solutions where all particles perform the same motion
shifted in time, and nonuniform sliding states, which are quasi-periodic
solutions where the system forms patterns of domains of different uniform
sliding states. We discuss the properties of this kind of pattern formation and
derive equations of motion for the slowly varying average particle density and
velocity. To observe these dynamical domains we suggest experiments with a
discrete ring of at least fifty Josephson junctions.
