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

Lufang Mi | Zendy; Wenyan Cui | Zendy; Honglian You | Zendy

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

Author(s) -

Lufang Mi,

Wenyan Cui,

Honglian You

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20190152

Subject(s) - periodic boundary conditions , lambda , mathematics , mathematical analysis , swift , partial differential equation , boundary value problem , physics , quantum mechanics , astrophysics

In this paper, we consider the complex Swift-Hohenberg(CSH) equation ∂u ∂t = λu − (α + iβ) ( 1 + ∂ 2 ∂x2 )2 u − (σ + iρ)|u|u 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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