Asymptotic linearization of the Fisher equation for a class of initial conditions

Puri, S. ; Bray, A. J. (1994) Asymptotic linearization of the Fisher equation for a class of initial conditions Journal of Physics A: Mathematical and General, 27 (2). pp. 453-460. ISSN 0305-4470

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Official URL: http://iopscience.iop.org/0305-4470/27/2/028/

Related URL: http://dx.doi.org/10.1088/0305-4470/27/2/028

Abstract

We present a novel method of linearizing the Fisher equation asymptotically in time, i.e. we use a nonlinear transformation to convert the initial value problem for the Fisher equation into an initial value problem for the diffusion equation for a class of initial conditions. The analytic result we obtain is in excellent agreement with numerical simulations. Our method easily generalizes to other reaction-diffusion equations also.

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