Traveling wave solutions for an autocatalytic reaction–diffusion model

In this paper we consider an autocatalytic reaction–diffusion model which has many applications. We extend previous results using qualitative analysis and show the existence of an exponentially decaying traveling wave front for a minimum speed and algebraically decaying wave fronts for large speeds. Further, the wave front profiles are calculated and the minimum speed is accurately determined using different numerical methods.

► This paper considers the autocatalytic reaction–diffusion model.
► The existence of traveling wave solutions are shown.
► The wave profiles are calculated and a minimum speed is accurately determined.