Existence of travelling wave solutions for a Fisher–Kolmogorov system with biomedical applications

•We calculate exact solutions of our simplified model.•We prove the existence of heteroclinic connections in our general model.•We prove the existence of traveling fronts for our biological general model, using singular perturbation techniques.

We consider a Fisher-Kolmogorov system with applications in oncology Pérez-García et al. (2015). Of interest is the question of the existence of travelling front solutions of the system. When the speed of the travelling wave is sufficiently large, existence of such fronts is shown using singular geometric perturbation theory.