TRAVELING WAVE SOLUTIONS FOR A CHEMOTAXIS SYSTEM

In this article we study the existence of traveling wave solutions for a system of equations modeling one-dimensional movement of bacteria, driven by an existing substrate. We propose a class of chemotactic coefficients depending on two parameters m and p. According to the values of these coefficients, as well as to the diffusion parameters (corresponding to the bacteria and to the substrate), we prove existence and properties of traveling wave solutions, and even (in very special cases) provide explicit solutions.