In this paper, we prove an abstract KAM (Kolmogorov–Arnold–Moser) theorem for infinite dimensional reversible Schrödinger systems. Using this KAM theorem together with partial Birkhoff normal form method, we obtain the existence of quasi-periodic solutions for a class of completely resonant reversible coupled nonlinear Schrödinger systems on two dimensional torus.

中文翻译：

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二维完全共振可逆Schrödinger系统的KAM定理

在本文中，我们证明了用于无限维可逆Schrödinger系统的抽象KAM（Kolmogorov–Arnold–Moser）定理。使用此KAM定理和部分Birkhoff正态形式方法，我们获得了一类在二维圆环上的完全共振可逆耦合非线性Schrödinger系统的拟周期解的存在。