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 tumor growth and invasion based on the model introduced by Chaplain and Lolas for the case of one spatial 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 nonnegative functions depending on the traveling wave variable with certain conditions imposed on model parameters.