Fisher's equation

Summary

Fisher's equation, also called the KPP–Fisher equation, is the scalar reaction–diffusion equation $u_t = D u_{xx} + r u(1 - u)$. It couples diffusion with logistic growth. It was proposed by Fisher in 1937 for the spread of an advantageous gene, and studied in the same year by Kolmogorov, Petrovsky and Piskunov. It is the model example of an equation with travelling wave fronts that invade an unstable state.