  Frictional sliding is an intrinsically complex phenomenon, emerging from the
interplay between driving forces, elasto-frictional instabilities, interfacial
nonlinearity and dissipation, material inertia and bulk geometry. We show that
homogeneous rate-and-state dependent frictional systems, driven at a prescribed
boundary velocity -- as opposed to a prescribed stress -- in a range where the
frictional interface is rate-weakening, generically host self-healing slip
pulses, a sliding mode not yet fully understood. Such velocity-driven
frictional systems are then shown to exhibit coarsening dynamics saturated at
the system length in the sliding direction, independently of the system's
height, leading to steadily propagating pulse trains. The latter may be viewed
as a propagating phase-separated state, where slip and stick characterize the
two phases. While pulse trains' periodicity is coarsening-limited by the
system's length, the single pulse width, characteristic slip velocity and
propagation speed exhibit rich properties, which are comprehensively understood
using theory and extensive numerics. Finally, we show that for sufficiently
small system heights, pulse trains are accompanied by periodic
elasto-frictional instabilities.
