  We prove the existence of fast traveling pulse solutions in excitable media
with non-local coupling. Existence results had been known, until now, in the
case of local, diffusive coupling and in the case of a discrete medium, with
finite-range, non-local coupling. Our approach replaces methods from geometric
singular perturbation theory, that had been crucial in previous existence
proofs, by a PDE oriented approach, relying on exponential weights, Fredholm
theory, and commutator estimates.
