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Validity of the linear marginal stability principle for monotonic fronts of the extended Fisher-Kolmogorov equation

R. D. Benguria·M. C. Depassier
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Abstract

The extended Fisher Kolmogorov equation $u_t = u_{xx} - γu_{xxxx} + f(u)$ with arbitrary positive $f(u)$, satisfying $f(0) = f(1) =0$, has monotonic traveling fronts for $γ< 1/12$. We find a simple lower bound on the speed of the fronts which allows to assess the validity of linear marginal stability.

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R. D. Benguria, M. C. Depassier. 2005-03-10. Validity of the linear marginal stability principle for monotonic fronts of the extended Fisher-Kolmogorov equation. https://arxiv.org/abs/nlin/0503025

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