Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2025-05-05 DOI:10.1007/s13540-025-00409-1

Jieyu Liu, Jing Zhang

引用次数: 0

Abstract

In this paper, we focus on a type of fractional nonlinear Schrödinger equation with odd periodic boundary conditions, where the nonlinearity periodically depending on spatial variable x. By an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems with unbounded perturbation, we obtain that there exists a lot of smooth quasi-periodic solutions with small amplitude for fractional nonlinear Schrödinger equations.

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具有周期性依赖于空间变量非线性的分数阶非线性Schrödinger方程的不变环面

本文研究一类具有奇周期边界条件的分数阶非线性Schrödinger方程，其非线性周期依赖于空间变量x。利用无界扰动下无限维可逆系统的KAM （Kolmogorov-Arnold-Moser）抽象定理，得到了分数阶非线性Schrödinger方程存在许多小振幅的光滑拟周期解。

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.