Reducible KAM tori for two-dimensional nonlinear Schrodinger equations with explicit dependence on the spatial variable

被引：3

作者：

Geng, Jiansheng ^{[1
]}

Xue, Shuaishuai ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Nanjing Audit Univ, Sch Stat & Math, Nanjing 211815, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 282卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Schrodinger equation; KAM tori; Quasi-periodic solutions; QUASI-PERIODIC SOLUTIONS; COMPACT LIE-GROUPS; WAVE-EQUATIONS; HAMILTONIAN PERTURBATIONS; DIMENSIONAL TORI; THEOREM; CONSTRUCTION; SYSTEMS; NLS;

D O I：

10.1016/j.jfa.2022.109430

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the two-dimensional nonlinear Schrodinger equation iu(t) -Delta u + |u|(2)u partial derivative integral (x, u, u )/partial derivative u = 0, t is an element of R, x is an element of T-2 with periodic boundary conditions. The nonlinearity f (x, u, u) =Sigma(j,l,j+l >= 6) a(jl)(x)u(j)u, a(jl) = a(lj) is a real analytic function 6 in a neighborhood of the origin. We obtain, through an infinite dimensional KAM theorem, a Whitney smooth family of small-amplitude quasi-periodic solutions. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：51

共 45 条

[41] Xu JX, 1996, SCI CHINA SER A, V39, P384
[42] Xu JX, 1996, SCI CHINA SER A, V39, P372
[43] Persistence of Louver-dimensional tori under the first Melnikov's non-resonance condition
Xu, JX
You, JG
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2001, 80 (10): : 1045 - 1067
[44] Perturbations of lower dimensional tori for Hamiltonian systems
You, JG
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 152 (01) : 1 - 29
[45] Quasi-periodic solutions of completely resonant nonlinear wave equations
Yuan, Xiaoping
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 230 (01) : 213 - 274

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