PERIODIC AND QUASI-PERIODIC SOLUTIONS FOR THE COMPLEX SWIFT-HOHENBERG EQUATION

Lufang Mi; Wenyan Cui; Honglian You

doi:10.11948/20190152

2020 Volume 10 Issue 1

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Lufang Mi, Wenyan Cui, Honglian You. PERIODIC AND QUASI-PERIODIC SOLUTIONS FOR THE COMPLEX SWIFT-HOHENBERG EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 297-313. doi: 10.11948/20190152

Citation:

Lufang Mi, Wenyan Cui, Honglian You. PERIODIC AND QUASI-PERIODIC SOLUTIONS FOR THE COMPLEX SWIFT-HOHENBERG EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 297-313. doi: 10.11948/20190152

PERIODIC AND QUASI-PERIODIC SOLUTIONS FOR THE COMPLEX SWIFT-HOHENBERG EQUATION

1.
College of Science, The Institute of Aeronautical Engineering and Technology, Binzhou University, Shandong Province, 256600, China
2.
College of Science, Binzhou University, Shandong Province, 256600, China

Corresponding author: Email address: yufengxingshi@163.com(W. Cui)
Fund Project: The authors were supported by NNSFC(11601036, 11401041), NSFSP(ZR2019MA062), Science and Technology Foundation of Shandong Province(J16LI52) and Binzhou University (BZXYL1704)

Abstract

Abstract

In this paper, we consider the complex Swift-Hohenberg(CSH) equation $ \frac{\partial u}{\partial t} = \lambda u-(\alpha+\mathrm{i}\beta)\left(1+\frac{\partial^2}{\partial x^2}\right)^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.
- Complex Swift-HohenbergC equation /
- periodic solution /
- quasi-periodic solution /
- normal form
MSC: 37K55, 35Q53

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References

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