Uniqueness of solutions for the extended Fisher-Kolmogorov equation |
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| Affiliation: | 1. School of Mathematics, Hunan University, Changsha 410082, China;2. Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Changsha 410082, China |
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| 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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