Quasi-periodic solutions in a nonlinear Schrödinger equation
Quasi-periodic solutions in a nonlinear Schrödinger equation
复制标题
DOI：
10.1016/j.jde.2006.07.027
复制
发表时间：
2007-02
影响因子：
2.4
通讯作者：
J. Geng;Y. Yi
中科院分区：
文献类型：
--
作者：
J. Geng;Y. Yi
本文研究了一维非线性薛定谔方程周期边界条件。证明了对于任意给定的常位势m和任意给定的整数N>1，该方程存在一个Whitney光滑的具有N个丢番图频率的小振幅时间拟周期解族.证明是基于部分Birkhoff规范形式减少和改进的KAM方法。
In this paper, one-dimensional (1D) nonlinear Schrödinger equation with the periodic boundary condition is considered. It is proved that for each given constant potential m and each prescribed integer N>1, the equation admits a Whitney smooth family of small amplitude, time quasi-periodic solutions with N Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method.