On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity

被引：2
|
作者：
Shi, Yanling [1 ]
Xu, Junxiang [2 ]
Xu, Xindong [2 ]
机构：
[1] Yancheng Inst Technol, Dept Basic Sci, Yancheng 224051, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2015年 / 56卷 / 02期
关键词：
PARTIAL-DIFFERENTIAL-EQUATIONS; WAVE EQUATIONS; KAM THEOREM; HAMILTONIAN PERTURBATIONS; STRONG INSTABILITY; SOLITARY WAVES; BLOW-UP;
D O I：
10.1063/1.4906810
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, one-dimensional generalized Boussinesq equation: u(tt) - u(xx) + (u(2) + u(xx))(xx) = 0 with boundary conditions u(x)(0,t) = u(x)(pi,t) = u(xxx)(0, t) = u(xxx)(pi, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form. (C) 2015 AIP Publishing LLC.
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页数：15
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