An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
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DOI：
10.1016/j.aim.2011.01.013
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发表时间：
2011-04
影响因子：
1.7
通讯作者：
J. Geng;Xindong Xu;J. You
中科院分区：
文献类型：
--
作者：
J. Geng;Xindong Xu;J. You
我们证明了一个无限维KAM定理。作为应用，我们将该定理应用于二维非线性薛定谔方程周期边界条件的研究。我们得到的方程的小振幅准周期解对应于有限维不变环面相关联的无限维动力系统的惠特尼光滑家庭。
We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the two dimensional nonlinear Schrödinger equation with periodic boundary conditions. We obtain for the equation a Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.