一类导数非线性薛定谔方程的拟周期解
Quasi-periodic Solutions of a Derivative Nonlinear Schrödinger Equation
摘要：
本文研究了一维非线性薛定谔方程的周期边界条件\begin{equation*} \mi u_t+u_{xx}+\mi |u|^2u_x=0, \ \ x\in \mathbb{T}:=\mathbb{R}/2π\mathbb{Z}. \end{equation*}，证明了该方程存在一族具有两个丢番图频率的实解析拟周期解.证明是基于部分Birkhoff标准形和KAM方法。
英文摘要：
This paper is concerned with a one dimensional (1D) derivative nonlinear Schrödinger equation with periodic boundary conditions \begin{equation*} \mi u_t+u_{xx}+\mi |u|^2u_x=0, \ \ x\in \mathbb{T}:=\mathbb{R}/2π\mathbb{Z}. \end{equation*} We show that above equation admits a family of real analytic quasi-periodic solutions with two Diophantine frequencies. The proof is based on a partial Birkhoff normal form and KAM method.
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