Front form and velocity in a one-dimensional autocatalytic [Formula Presented] reaction

We consider the general irreversible [Formula Presented] autocatalytic reaction in one dimension, for which the corresponding diffusion constants [Formula Presented] and [Formula Presented] may differ. Contrary to mean-field-type predictions, the Monte Carlo simulations show that, as long as [Formula Presented] only a unique, stable front propagates with constant velocity. When [Formula Presented] the behavior changes drastically: both the front’s position and its characteristic width grow with [Formula Presented] These findings are adequately described within a Smoluchowski-type approach.