KAM THEORY FOR A NONLINEAR SCHRODINGER EQUATION WITH ALMOST-PERIODIC FORCING

被引：0

作者：

Rui, Jie ^{[1
]}

Zhu, Sixue ^{[1
]}

Zhang, Tingting ^{[2
]}

Zhang, Min ^{[1
]}

机构：

[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[2] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年

关键词：

Nonlinear Schrodinger equations; almost-periodic solutions; Diophan-; tine frequencies; KAM theorem; almost-periodic forcing; INVARIANT TORI; FULL DIMENSION;

D O I：

10.3934/dcdsb.2024125

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop an infinite dimensional Kolmogorov-Arnold-Moser theorem. As an application, we prove the existence of almost-periodic solutions for a nonlinear Schr & ouml;dinger equation iu(t )- u(xx )+ mu u + psi(omega t) f(|u|(2))u = 0, mu > 0, t is an element of R, x is an element of [0, 2 pi] subject to periodic boundary conditions, where psi(omega t) is analytic and almost-periodic, f is real analytic in some neighborhood of the origin. For some technical difficulties in some known results, the almost-periodic potential requires a special structure. The overall strategy to overcome such difficulties is the set of Diophantine frequencies inspired by Montalto and Procesi

引用

页数：25

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