Title: Exact traveling wave solutions of 1D model of cancer invasion,
Abstract: In this paper we consider the continuous mathematical model of tumour growth
and invasion based on the model introduced by Anderson, Chaplain et al.
\cite{Anderson&Chaplain2000}, for the case of one space dimension. The model
consists of a system of three coupled nonlinear reaction-diffusion-taxis
partial differential equations describing the interactions between cancer
cells, the matrix degrading enzyme and the tissue. For this model under certain
conditions on the model parameters we obtain the exact analytical solutions in
terms of traveling wave variables. These solutions are smooth positive definite
functions whose profiles agree with those obtained from numerical computations
\cite{Chaplain&Lolas2006} for not very large time intervals.