KAM theorems for nonlinear higher dimensional Schrödinger equation systems in three different ways

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-04 DOI:10.1016/j.cnsns.2025.108981

Ningning Chang , Yingnan Sun

引用次数: 0

Abstract

We prove an abstract KAM (Kolmogorov–Arnold–Moser) theorem constructed by Zhou (2017) in different ways and apply it to the nonlinear Schrödinger equation systems with real Fourier Multiplier. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions for more types of equation systems.

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非线性高维Schrödinger方程系统的三种不同方法的KAM定理

我们以不同的方式证明了Zhou（2017）构造的抽象KAM （Kolmogorov-Arnold-Moser）定理，并将其应用于具有实数傅里叶乘数的非线性Schrödinger方程系统。证明了一类多类型方程组的惠特尼光滑小振幅拟周期解的存在性。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.