Almost-periodic solutions for a quasi-periodically forced nonlinear Schrodinger equation

被引：0

作者：

Liu, Shujuan ^{[1
]}

机构：

[1] Hunan Normal Univ, Key Lab High Performance Comp & Stochast Informat, Dept Math, Changsha 410083, Hunan, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2022年 / 53卷 / 01期

关键词：

Quasi-periodically forced; KAM theory; Schrodinger equation; Almost-periodic solution; INVARIANT TORI; FULL DIMENSION; CONSTRUCTION;

D O I：

10.1007/s13226-021-00098-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the existence of small amplitude solutions which are almost-periodic in time for a quasi-periodically forced nonlinear Schrodinger equation root-1u(t) - u(xx) + M(xi)u + f((omega) over tildet vertical bar u vertical bar(2)u = 0 with periodic boundary conditions u(t, x + 2 pi) = u(t, x), t is an element of R, where M-xi is a real Fourier multiplier, f((theta) over tilde) ((theta) over tilde = (omega) over tildet) real analytic and the forced frequency vector (omega) over tilde is an element of R-b is fixed and Diophantine.

引用

页码：10 / 31

页数：22

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