Superfast front propagation in reactive systems with non-Gaussian diffusion

We study a reactive field transported by a non-Gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with exponential tails, the usual qualitative behaviour of the standard reaction diffusion system, i.e. , exponential tails for the reacting field and a constant front speed, are recovered. But, if the process has power law tails and the reaction is pulled, the reacting field shows power law tails and the front speed increases exponentially with time. The comparison with other transport processes which exhibit anomalous diffusion shows that not only the presence of anomalous diffusion, but also its detailed mechanism, is relevant for the front propagation in reactive systems.