Traveling waves in a one-dimensional integrate-and-fire neural network with finite support connectivity

We study the existence of traveling waves in a one-dimensional network of integrateand-fire neurons with finite support coupling. We show that when the reset after spiking is sufficiently low, the interspike intervals (ISIs) for a traveling wave with an explicit first wave front can be computed. Further, we analytically derive a self-consistency equation that generates an explicit dispersion relation between the velocity of periodic traveling waves and their corresponding ISIs. Finally, we prove that the ISIs of non-periodic traveling waves converge to the ISI of the periodic waves with the same speed.