Quasi-periodic Solutions of a Derivative Nonlinear Schr\"odinger Equation
Dynamical Systems
2015-04-09 v1
Abstract
This paper is concerned with a one dimensional (1D) derivative nonlinear Schr\"odinger equation with periodic boundary conditions \begin{equation*} \mi u_t+u_{xx}+\mi |u|^2u_x=0, \ \ x\in \mathbb{T}:=\mathbb{R}/2\pi\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.
Keywords
Cite
@article{arxiv.1407.0910,
title = {Quasi-periodic Solutions of a Derivative Nonlinear Schr\"odinger Equation},
author = {Jie Liu},
journal= {arXiv preprint arXiv:1407.0910},
year = {2015}
}
Comments
30 pages