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

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

2005-03-10

arxiv.org/abs/nlin/0503025v1

Nonlinear Sciences

Pattern Formation and Solitons

3 pages, no figures

Scientific paper

The extended Fisher Kolmogorov equation $u_t = u_{xx} - \gamma u_{xxxx} +
f(u)$ with arbitrary positive $f(u)$, satisfying $f(0) = f(1) =0$, has
monotonic traveling fronts for $\gamma < 1/12$. 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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