A geometric construction of travelling wave solutions to the   Keller-Segel model
  We study a version of the Keller-Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit. 
Kristen Harley, Peter van Heijster and Graeme Pettet
math.DS