Perturbative linearization of reaction-diffusion equations

Abstract

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction–diffusion systems, namely the Fisher equation and the time-dependent Ginzburg-Landau equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction-diffusion equations into the solution of a hierarchy of linear equations. Our numerical results demonstrate that this hierarchy rapidly converges to the exact solution.