Abstract
We consider stationary solutions of the Extended Fisher-Kolmogorov (EFK) equation, a fourth-order model equation for bi-stable systems. We show that as long as the stable equilibrium points are real saddles, the paths in the ( u, u')-plane of two bounded solutions do not cross. As a consequence we derive that the bounded solutions of the EFK equation correspond exactly to those of the classical Fisher-Kolmogorov equation.
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