Quasi-periodic solutions in a nonlinear Schrodinger equation

被引：67

作者：

Geng, Jiansheng

Yi, Yingfei ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 233卷 / 02期

基金：

美国国家科学基金会;

关键词：

Schrodinger equation; Hamiltonian systems; KAM theory; normal form; quasi-periodic solution;

D O I：

10.1016/j.jde.2006.07.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, one-dimensional (1D) nonlinear Schrodinger equation iu(t) - u(xx) + mu + vertical bar u vertical bar(4)u = 0 with the periodic boundary condition is considered. It is proved that for each given constant potential m and each prescribed integer N > 1, the equation admits a Whitney smooth family of small amplitude, time quasi-periodic solutions with N Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：512 / 542

页数：31

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