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arXiv · 2404.05066

Entire solutions to the Swift--Hohenberg equation via variational approach

S. B. Kolonitskii·L. M. Lerman·A. I. Nazarov
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Abstract

We study the stationary Swift--Hohenberg equation $(\Delta + 1)^2 u - \alpha u - \beta u^2 + u^3=0$ in the whole space $\mathbb R^n$, $2\le n \le 7$. 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.

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S. B. Kolonitskii, L. M. Lerman, A. I. Nazarov. 2024-04-07. Entire solutions to the Swift--Hohenberg equation via variational approach. https://arxiv.org/abs/2404.05066

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