| Volume 10, Number 1, 2020, Pages 297-313 DOI：10.11948/20190152 |
| Periodic and quasi-periodic solutions for the complex Swift-Hohenberg equation |
| Lufang Mi,Wenyan Cui,Honglian You |
| Keywords:Complex Swift-HohenbergC equation, periodic solution, quasi-periodic solution, normal form. |
| Abstract: |
| In this paper, we consider the complex Swift-Hohenberg(CSH) equation $\frac{\partial u}{\partial t}=\lambda u-(\alpha+\mathrm{i}\beta)\l(1+\frac{\partial^2}{\partial x^2}\r)^2u-(\sigma+\mathrm{i}\rho)|u|^2u $ subject to periodic boundary conditions. Using an infinite dimensional KAM theorem, we prove that there exist a continuous branch of periodic solutions and a Cantorian branch of quasi-periodic solutions for
the above equation. |
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