Quasi-periodic Solutions of a Derivative Nonlinear Schrödinger Equation
arXiv:1407.0910 · doi:10.1080/00036811.2015.1032942
Abstract
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.
30 pages