Exact traveling wave solutions of one-dimensional models of cancer invasion

In this paper we obtain exact analytical solutions of equations of continuous mathematical models of tumour growth and invasion based on the model introduced by Chaplain and Lolas for the case of one space dimension. The models consist of a system of three nonlinear reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, the matrix degrading enzyme and the tissue. The obtained solutions are smooth non-negative functions depending on the traveling wave variable and certain conditions on the model parameters.