The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation

被引：6
作者：
Cong, Hongzi [1 ]
Yuan, Xiaoping [2 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Liaoning, Peoples R China
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2021年 / 38卷 / 03期
基金：
中国国家自然科学基金;
关键词：
KAM theory; Almost periodic solution; Nonlinear wave equation; Gevrey space;
D O I：
10.1016/j.anihpc.2020.09.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we prove the existence and linear stability of full dimensional tori with subexponential decay for 1-dimensional nonlinear wave equation with external parameters, which relies on the method of KAM theory and the idea proposed by Bourgain [9]. (C) 2020 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：759 / 786
页数：28
相关论文
共 26 条
  • [1] Time quasi-periodic gravity water waves in finite depth
    Baldi, Pietro
    Berti, Massimiliano
    Haus, Emanuele
    Montalto, Riccardo
    [J]. INVENTIONES MATHEMATICAE, 2018, 214 (02) : 739 - 911
  • [2] KAM for autonomous quasi-linear perturbations of KdV
    Baldi, Pietro
    Berti, Massimiliano
    Montalto, Riccardo
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (06): : 1589 - 1638
  • [3] KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation
    Baldi, Pietro
    Berti, Massimiliano
    Montalto, Riccardo
    [J]. MATHEMATISCHE ANNALEN, 2014, 359 (1-2) : 471 - 536
  • [4] Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential
    Berti, Massimiliano
    Bolle, Philippe
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (01) : 229 - 286
  • [5] Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
    Berti, Massimiliano
    Bolle, Philippe
    [J]. NONLINEARITY, 2012, 25 (09) : 2579 - 2613
  • [6] Biasco J.E.M.L., 2019, ARXIV190307576
  • [7] Construction of approximative and almost periodic solutions of perturbed linear Schrodinger and wave equations
    Bourgain, J
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 1996, 6 (02) : 201 - 230
  • [8] On invariant tori of full dimension for 1D periodic NLS
    Bourgain, J
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 229 (01) : 62 - 94
  • [9] Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrodinger equations
    Bourgain, J
    [J]. ANNALS OF MATHEMATICS, 1998, 148 (02) : 363 - 439
  • [10] Bourgain J., 2005, Ann. of Math. Stud., V158
123