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Spatial patterns described by the extended Fisher-Kolmogorov equation: Periodic solutions. (English) Zbl 0891.34048
Summary: Stationary antisymmetric single-bump periodic solutions of a fourth-order generalization of the Fisher-Kolmogorov (FK) equation are analyzed. The coefficient γ>0 of the additional fourth-order spatial derivative is found to be a critical parameter. If γ1 8, the family of periodic solutions is still very similar to that of the FK equation. However, if γ>1 8, it is possible to distinguish different families of periodic solutions and the structure of such solutions is much richer.

34C25Periodic solutions of ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
35Q35PDEs in connection with fluid mechanics
60E99Distribution theory in probability theory