A DEGENERATE KAM THEOREM FOR PARTIAL DIFFERENTIAL EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

被引：4

作者：

Gao, Meina ^{[1
]}

Liu, Jianjun ^{[2
]}

机构：

[1] Shanghai Polytech Univ, Coll Arts & Sci, Shanghai 201209, Peoples R China

[2] Sichuan Univ, Sch Math, Chengdu 610065, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 10期

关键词：

Degenerate KAM theory; multiple normal frequencise; NONLINEAR SCHRODINGER-EQUATION; PLANE-WAVE SOLUTIONS; SOBOLEV STABILITY; PERTURBATIONS;

D O I：

10.3934/dcds.2020252

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an infinite dimensional KAM theorem with double normal frequencies is established under qualitative non-degenerate conditions. This is an extension of the degenerate KAM theorem with simple normal frequencies in [3] by Bambusi, Berti and Magistrelli. As applications, for nonlinear wave equation and nonlinear Schrodinger equation with periodic boundary conditions, quasi-periodic solutions of small amplitude and quasi-periodic solutions around plane wave are obtained respectively.

引用

页码：5911 / 5928

页数：18

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