Quasi-periodic solutions of fractional nonlinear Schrodinger equation systems
Quasi-periodic solutions of fractional nonlinear Schrodinger equation systems
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分数阶非线性薛定谔方程组的准周期解
DOI：
10.1080/00036811.2020.1800648
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发表时间：
2020
影响因子：
1.1
通讯作者：
Shi Yanling
中科院分区：
文献类型：
--
作者：
Shi Yanling
本文研究了具有周期边界条件的分数阶非线性薛定谔方程组。建立了一个抽象的无穷维KAM定理，并将其应用于含真实的Fourier乘子的分数阶非线性薛定谔方程组。通过建立块对角规范形，证明了相应的无穷维动力系统的有限维不变环面上存在一类Whitney光滑的小振幅拟周期解族.
In this paper, the fractional nonlinear Schrödinger equation system with periodic boundary conditions is considered. I establish an abstract infinite-dimensional KAM theorem and apply it to fractional nonlinear Schrödinger equation system with real Fourier multiplier. By establishing a block diagonal normal form, we prove the existence of a class of Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite-dimensional invariant tori of an associated infinite-dimensional dynamic system.