Travelling waves in non-local reaction-dispersion equations with diffuse levy measures

In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In particular, we review the results that already exist in the literature and complete the table. It appears that the most important case is that of a bistable nonlinearity, which we then extend to other classical nonlinearities.