3 papers
math.AP2020
Birkhoff Normal Form for the Derivative Nonlinear Schrödinger Equation
Jianjun Liu
This paper is concerned with the derivative nonlinear Schrödinger equation with periodic boundary conditions. We obtain complete Birkhoff normal form of order six. As an applicatio…
math.DS2018
Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrodinger equation
Meina Gao, Jianjun Liu
This paper is concerned with the derivative nonlinear Schrodinger equation with periodic boundary conditions $$\mathbf{i}u_t+u_{xx}+\mathbf{i}\Big(f(x,u,\bar{u})\Big)_x=0,\quad x\i…
math.DS2017
The Stability of Full Dimensional KAM tori for Nonlinear Schrödinger equation
Hongzi Cong, Jianjun Liu, Yunfeng Shi +1
In this paper, it is proved that the full dimensional invariant tori obtained by Bourgain [J. Funct. Anal., \textbf{229} (2005), no. 1, 62-94.] is stable in a very long time for 1D…