Perturbative Linearization of Reaction-Diffusion Equations

Sanjay Puri , Kay Joerg Wiese (1, 2)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 KITP

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) 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.

Domaines: Autre [cond-mat.other]

Sanjay Puri, Kay Joerg Wiese. Perturbative Linearization of Reaction-Diffusion Equations. 2002. ⟨hal-00283822⟩