Key points are not available for this paper at this time.
We study the stationary Swift--Hohenberg equation (+ 1) ² u - u - u² + u³=0 in the whole space Rⁿ, 2 n 7. We develop and modify the variational approach introduced by Lerman, Naryshkin and Nazarov (2020) and obtain a series of periodic solutions with certain additional symmetries.
Kolonitskii et al. (Sun,) studied this question.