KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions
KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions
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DOI：
10.1016/j.jde.2013.11.007
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发表时间：
2014-02
影响因子：
2.4
通讯作者：
Jianjun Liu;Xiaoping Yuan
中科院分区：
文献类型：
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作者：
Jianjun Liu;Xiaoping Yuan
本文研究了一类周期边值条件为Iut+ux x+i(f(|u|2)u)x=0，x∈T：=R/2πZ的导数非线性薛定谔方程，其中f是C中原点附近的实解析解，f(0)=0，f‘(0)≠0.证明了上述方程具有小振幅的康托尔族光滑拟周期解。证明是基于无界扰动向量场的无穷维KAM定理。
This paper is concerned with the derivative nonlinear Schrödinger equation with periodic boundary conditions i u t+ u x x+ i (f (| u| 2) u) x= 0, x∈ T:= R/2 π Z, where f is real analytic in some neighborhood of the origin in C, f (0)= 0, and f′(0)≠ 0. We show the above equation possesses Cantor families of smooth quasi-periodic solutions of small amplitude. The proof is based on an infinite dimensional KAM theorem for unbounded perturbation vector fields.