On Traveling Wave Fronts in a Bacterial Growth Model with Density-Dependent Diffusion and Chemotaxis

Bacterial colonies often generate patterns that are characterized by fingerlike projections growing out of the propagating front. In this paper, we analyze the traveling wave fronts in bacterial growth model that accounts for chemotactic movement as well as random motion in density-dependent diffusion. Specifically, the existence of traveling wave solutions to model equations is examined by means of methods of local linear and nonlinear analysis, and numerical simulations. The occurrence is shown of both sharp and smooth traveling wave fronts.