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
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页数：25
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