A Novel Solution for the General Diffusion

Abstract

The Fisher-KPP equation is a reaction-diffusion equation originally proposed by Fisher to represent allele propagation in genetic hosts or population. It was also proposed by Kolmogorov for more general applications. A novel method for solving nonlinear partial differential equations is applied to produce a unique, approximate solution for the Fisher-KPP equation. Analysis proves the solution is counterintuitive. Although still satisfying the maximum principle, time dependence collapses for all time greater than zero, therefore, the solution is highly irregular and not smooth, invalidating the traveling wave approximation so often employed.