  We study Class-I excitable $1$-dimensional media showing the appearance of
propagating traveling pulses. We consider a general model exhibiting Class-I
excitability mediated by two different scenarios: a homoclinic (saddle-loop)
and a SNIC (Saddle-Node on the Invariant Circle) bifurcations. The distinct
properties of Class-I with respect to Class-II excitability infer unique
properties to traveling pulses in Class-I excitable media. We show how the
pulse shape inherit the infinite period of the homoclinic and SNIC bifurcations
at threshold, exhibiting scaling behaviors in the spatial thickness of the
pulses that are equivalent to the scaling behaviors of characteristic times in
the temporal case.
