Existence and Stability of Traveling Fronts in the Extended Fisher–Kolmogorov Equation

We study traveling wave solutions to a general fourth-order differential equation that is a singular perturbation of the Fisher–Kolmogorov equation. We apply the geometric method for singularly perturbed systems to show that for every positive wavespeed there exists a traveling wave. Also, we find t...

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Bibliographic Details
Published in:Journal of Differential Equations 2001-11, Vol.176 (2), p.532-560
Main Authors: Rottschäfer, V., Wayne, C.E.
Format: Article
Language:English
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Summary:We study traveling wave solutions to a general fourth-order differential equation that is a singular perturbation of the Fisher–Kolmogorov equation. We apply the geometric method for singularly perturbed systems to show that for every positive wavespeed there exists a traveling wave. Also, we find that there exists a critical wavespeed c* which divides these solutions into monotonic (c⩾c*) and oscillatory (c
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.2000.3984