QUASI-PERIODIC SOLUTIONS OF GENERALIZED BOUSSINESQ EQUATION WITH QUASI-PERIODIC FORCING

被引：6

作者：

Shi, Yanling ^{[1
]}

Xu, Junxiang ^{[2
]}

Xu, Xindong ^{[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 | 2017年 / 22卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Quasi-periodically forced generalized Boussinesq equation; quasi-periodic solution; infinite dimensional KAM theory; invariant torus; WAVE-EQUATIONS; BLOW-UP; STRONG INSTABILITY; GLOBAL EXISTENCE; SOLITARY WAVES;

D O I：

10.3934/dcdsb.2017104

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, one-dimensional quasi-periodically forced generalized Boussinesq equation u(tt) - u(xx) + u(xxxx) + epsilon phi(t) (u + u(3))(xx) = 0 with hinged boundary conditions is considered, where epsilon is a small positive parameter, phi(t) is a real analytic quasi- periodic function in t with frequency vector omega = (omega(1), omega(2), ... ,omega(m)). It is proved that, under a suitable hypothesis on phi(t); there are many quasi- periodic solutions for the above equation via KAM theory.

引用

页码：2501 / 2519

页数：19

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