Quasi-periodic solutions of nonlinear Schrodinger equations on Td

被引：5

作者：

Berti, Massimiliano ^{[1
]}

Bolle, Philippe ^{[2
]}

机构：

[1] Univ Naples Federico 2, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

[2] Univ Avignon & Pays Vaucluse, Lab Anal Non Lineaire & Geometrie EA 2151, F-84018 Avignon, France

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2011年 / 22卷 / 02期

基金：

欧洲研究理事会;

关键词：

Nonlinear Schrodinger equation; Nash-Moser Theory; KAM for PDE; quasi-periodic solutions; small divisors; infinite dimensional Hamiltonian systems; WAVE EQUATIONS;

D O I：

10.4171/RLM/597

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present recent existence results of quasi-periodic solutions for Schrodinger equations with a multiplicative potential on T-d, d >= 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are in C-infinity then the solutions are in C-infinity. The proofs are based on an improved Nash-Moser iterative scheme and a new multiscale inductive analysis for the inverse linearized operators.

引用

页码：223 / 236

页数：14

共 20 条

[11]

Bourgain J, 2005, Annals of Mathematics Studies, V158

[12] NEWTONS METHOD AND PERIODIC-SOLUTIONS OF NONLINEAR-WAVE EQUATIONS [J].