Traveling Waves of Chemotaxis Model on Food Metric

In this paper, we are interested in the stability of traveling waves to a chemotaxis model arising from the food metric. The appropriate ansatz is employed to provide the traveling waves from the original chemotaxis model. The traveling waves in the ODE system are derived from the PDE system to establish the existence of the decoupled problem. Moreover, the appropriate Cole–Hopf transformation is applied to the original chemotaxis model to overcome the singularity. According to the regularity results, the traveling waves of the original and transformed problems, then the stability of the nonlinear traveling waves is proved.