THE CONSTRUCTION OF QUASI-PERIODIC SOLUTIONS OF QUASI-PERIODIC FORCED SCHRODINGER EQUATION

被引：14

作者：

Jiao, Lei ^{[1
]}

Wang, Yiqian ^{[1
]}

机构：

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

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 05期

关键词：

Hamiltonian systems; Schrodinger equation; KAM; normal form; NONLINEAR-WAVE EQUATIONS; BOUNDARY-CONDITIONS; KAM THEOREM; TORI;

D O I：

10.3934/cpaa.2009.8.1585

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct small amplitude quasi-periodic solutions for one dimensional nonlinear Schrodinger equation iu(t) = u(xx) - mu - f(beta t, x)vertical bar u vertical bar(2)u with the boundary conditions u(t, 0) = u(t, a pi) = 0, -infinity < t < infinity, where m is real and f(beta t, x) is real analytic and quasi-periodic on t satisfying the non-degeneracy condition lim(T ->infinity) 1/T integral(T)(0) f(beta t, x)dt equivalent to f(0) = const., 0 not equal f(0) is an element of R, with beta is an element of R(b) a fixed Diophantine vector.

引用

页码：1585 / 1606

页数：22

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