  We present a minimal one-dimensional model for the transition from crack-like
to pulse-like propagation of frictional rupture. In its non-dimensional form,
the model depends on only two free parameters: the non-dimensional pre-stress
and an elasticity ratio that accounts for the finite height of the system. The
model contains stable slip pulse solutions for slip boundary conditions, and
unstable slip pulse solutions for stress boundary conditions. Results
demonstrate that the existence of pulse-like ruptures requires only elastic
relaxation and redistribution of initial pre-stress. The novelty of our
findings is that pulse-like propagation along frictional interfaces is a
generic elastic feature, whose existence is not sensitive to particular rate-
or slip-dependencies of dynamic friction.
