Small-divisor Equation of Higher Order with Large Variable Coefficient and Application to the Coupled KdV Equation

In this paper, we establish an estimate for the solutions of small-divisor equation of higher order with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 27; no. 10; pp. 2005 - 2032
Main Authors Gao, Mei Na, Zhang, Jing
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.10.2011
Springer Nature B.V
Subjects
Boundary conditions
Coefficients
Estimates
Hilbert space
KAM定理
Mathematical analysis
Mathematics
Mathematics and Statistics
Perturbation methods
Studies
Theorems
公式
变系数
应用
无穷维
耦合KdV方程
除数
高阶
small-divisor equation with large variable coefficient
35B10
35B20
coupled KdV equation
KAM theorem
37K55
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Summary:In this paper, we establish an estimate for the solutions of small-divisor equation of higher order with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic solutions for the coupled KdV equation subject to small Hamiltonian perturbations.
Bibliography:11-2039/O1
In this paper, we establish an estimate for the solutions of small-divisor equation of higher order with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic solutions for the coupled KdV equation subject to small Hamiltonian perturbations.
KAM theorem, small-divisor equation with large variable coefficient, coupled KdV equation
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-0064-1