Painlev\'e analysis for two 1D parabolic-parabolic models of chemotaxis; some travelling wave solutions

TL;DR

This paper applies Painlevé analysis to two chemotaxis models, revealing conditions under which their reductions admit exact traveling wave solutions, thus advancing understanding of their analytical solvability.

Contribution

It introduces Painlevé analysis to chemotaxis models and identifies cases with exact traveling wave solutions, a novel approach in this context.

Findings

Certain reductions admit exact solutions

Painlevé analysis identifies integrable cases

Traveling wave solutions are explicitly constructed

Abstract

In this paper we study the Painlev\'e analysis for two models of chemotaxis. We find that in some cases the reductions of these models in terms of travelling wave variable allow exact analytical solutions.