Quasi-periodic Solutions of a Derivative Nonlinear Schr\"odinger   Equation
  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. 
Jie Liu
math.DS