Perturbative Linearization of Reaction-Diffusion Equations

Sanjay Puri1, Kay Jörg Wiese2
1School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India.
2KITP, Kohn Hall, University of California at Santa Barbara, Santa Barbara, CA 93106-4030, USA

Abstract

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.


cond-mat/0209524 [pdf]
J. Phys. A 36 (2003) 2043-2054 [pdf]


Copyright (C) by Kay Wiese. Last edited March 17, 2008.