A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse solutions along generic and realistic rate-and-state dependent frictional interfaces, separating large deformable bodies in contact. Such nonlinear interfaces feature a nonmonotonic frictional strength as a function of the slip velocity, with a local minimum. The solutions exhibit a diverging length and strongly inertial propagation velocities, when the driving stress approaches the frictional strength characterizing the local minimum from above, and change their character when it is away from it. An approximate scaling theory quantitatively explains these observations. The derived pulse solutions also exhibit significant spatially-extended dissipation in excess of the edge-localized dissipation (the effective fracture energy) and an unconventional edge singularity. The relevance of our findings for available observations is discussed.