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.

中文翻译：

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分数非线性薛定谔方程组的准周期解

在本文中，考虑了具有周期性边界条件的分数非线性薛定谔方程组。我建立了一个抽象的无限维KAM定理，并将其应用于具有实傅里叶乘数的分数非线性薛定谔方程组。通过建立块对角范式，我们证明了对应于关联的无限维动态系统的有限维不变环面的一类Whitney光滑族小幅度拟周期解的存在。