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.