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

R. D. Benguria, M. C. Depassier

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 $\gamma <1/12$.…