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 γ ≤ 1 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.
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Peletier et al. (1997) studied this question.
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