Almost periodic invariant tori for the NLS on the circle

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-01 DOI:10.1016/j.anihpc.2020.09.003

Luca Biasco, Jessica Elisa Massetti, Michela Procesi

引用次数: 17

Abstract

In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain in [15] on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract “counter-term theorem” à la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find “many more” almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.

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圆上NLS的几乎周期不变环面

本文研究了一类带外参数圆上NLS方程概周期解的存在性和线性稳定性。从Bourgain在[15]中关于五次NLS的开创性结果开始，我们提出了一种新的方法，允许在统一框架中证明有限维和无限维不变环面的持久性，这是期望解的支持。通过一个相当抽象的“逆项定理”，直接在原始椭圆变量中给出持久性结果，而不传递到作用角变量。我们的框架允许我们根据现有文献找到“更多”几乎周期性的解，并考虑非平移不变偏微分方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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