Traveling wave solutions of a nonlinear reaction–diffusion–chemotaxis model for bacterial pattern formation

In this paper we consider a nonlinear reaction–diffusion–chemotaxis model for the description of the spatiotemporal evolution of the bacteria of the type Paenibacillus dendritiformis on a thin layer of agar in a Petri dish. We perform a traveling wave analysis for the model equation showing the existence of traveling wave solutions, in particular, the sharp wave front type solutions with minimum speed. Further, we present numerical investigations for a special case. The minimum speed is estimated and the profile of the traveling wave solution is calculated and compared for different numerical methods.