Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation.

*(English)*Zbl 0862.34012The authors study spatial patterns of the bounded solutions of

$$\gamma {u}^{\text{'}\text{'}\text{'}\text{'}}={u}^{\text{'}\text{'}}+u-{u}^{3}\phantom{\rule{4.pt}{0ex}}\text{on}\phantom{\rule{4.pt}{0ex}}\mathbb{R}\xb7\phantom{\rule{2.em}{0ex}}(*)$$

The solutions of (*) exhibit a rich structure which depends crucially on the parameter $\gamma $. In fact one can have chaotic behavior in some sense which is defined in the paper (arbitrarily many maxima and minima). The proofs do not rely on abstract theorems but on clever constructive methods.

Reviewer: R.Sperb (Zürich)