QUASI-PERIODIC SOLUTIONS FOR A CLASS OF BEAM EQUATION SYSTEM

被引：2
|
作者：
Shi, Yanling [1 ]
Xu, Junxiang [2 ]
机构：
[1] Yancheng Inst Technol, Coll Math & Phys, Yancheng 224051, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 211189, Jiangsu, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 01期
关键词：
Beam equation system; quasi-periodic solution; infinite dimensional KAM theory; NONLINEAR-WAVE EQUATIONS; KAM THEOREM; HAMILTONIAN PERTURBATIONS; TORI;
D O I：
10.3934/dcdsb.2019171
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish an abstract infinite dimensional KAM theorem. As an application, we use the theorem to study the higher dimensional beam equation system {(u2tt + Delta 2u2 + mu u2 + u12u2 =) (0) (u1tt + Delta 2u1 + sigma u1 +u1u22 =0) under periodic boundary conditions, where 0 < sigma is an element of [sigma(1), sigma(2)], 0 < mu is an element of [mu(1), mu(2)] are real parameters. By establishing a block- diagonal normal form, we obtain the existence of a Whitney smooth family of small amplitude quasi- periodic solutions corresponding to fi nite dimensional invariant tori of an associated in fi nite dimensional dynamic system.
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页码：31 / 53
页数：23
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