# Exact traveling wave solutions of 1D parabolic-parabolic models of chemotaxis

## TL;DR

This paper derives exact analytical traveling wave solutions for three different one-dimensional parabolic-parabolic chemotaxis models, providing insights into their wave behaviors.

## Contribution

It introduces explicit traveling wave solutions for three distinct 1D chemotaxis models, advancing analytical understanding of these systems.

## Key findings

- Exact solutions in terms of traveling wave variables
- Analytical expressions for wave profiles
- Enhanced understanding of chemotactic wave dynamics

## Abstract

In this paper we consider three different 1D parabolic-parabolic systems of chemotaxis. For these systems we obtain the exact analytical solutions in terms of traveling wave variables.