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 that there exists a critical wavespeed c* which divides these solutions into monotonic (c⩾c*) and oscillatory (c