A KAM Theorem for Higher Dimensional Nonlinear Schrödinger Equations
A KAM Theorem for Higher Dimensional Nonlinear Schrödinger Equations
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DOI：
10.1007/s10884-013-9296-3
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发表时间：
2013-03
影响因子：
1.3
通讯作者：
J. Geng;J. You
中科院分区：
文献类型：
--
作者：
J. Geng;J. You
We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the higher dimensional nonlinear Schrödinger equation $$\begin{aligned} iu_t-\triangle u +M_\xi u+f(|u|^2)u=0, \quad t\in \mathbb{R }, x\in \mathbb{T }^d \end{aligned}$$with periodic boundary conditions, whereis a real Fourier multiplier andis a real analytic function nearwith. We obtain for the equation a Whitney smooth family of real-analytic small-amplitude linearly-stable quasi-periodic solutions with a nice linear normal form.
