The Kolmogorov–Petrovsky–Piskunov–Fisher (KPP-Fisher) equation is a nonlinear reaction-diffusion partial differential equation (PDE) with significant applications in population genetics, ecology, and combustion theory. The KPP-Fisher equation for a distribution combines a linear diffusion term with a nonlinear reaction term which is independent of the derivatives of the distribution. The standard analytical technique for solving the equation involves transforming it into a nonlinear ordinary differential equation by a change of variables and analyzing the resulting wave form. We demonstrate that an alternative approach inspired by non-classical symmetries but only using elementary methods leads to exact and closed form solutions for certain choices of boundary conditions. We exhibit this result with quadratic and cubic sources and in Cartesian and polar coordinates.

Faculty Mentor: Dr. Christopher Trombley

Department of Mathematics