Travelling waves in the Fisher–KPP equation with nonlinear degenerate or singular diffusion

We consider a one-dimensional reaction–diffusion equation of Fisher–Kolmogoroff– Petrovsky–Piscounoff type. We investigate the effect of the interaction between the nonlinear diffusion coefficient and the reaction termon the existence and non-existence of travelling waves. Our diffusion coefficient is allowed to be degenerate or singular at both equilibrium points, 0 and 1, while the reaction term need not be differentiable. These facts influence the existence and qualitative properties of travelling waves in a substantial way