A Constructive Approach to Traveling Waves in Chemotaxis

In this paper we study the existence of one-dimensional and multidimensional traveling wave solutions for general chemotaxis or so-called Keller-Segel models without reproduction of the chemotactic species. We present a constructive approach to give modelers a choice of chemotactic sensitivity functionals, production, and degradation terms for the chemical signal at hand. The main aim is to understand the type of functionals and the interplay between them that are needed for the traveling wave and pulse patterns to occur.