4 citations · 8 across the 6 of their papers we have counts for
6 papers
Exact Global Control of Small Divisors in Rational Normal Form
Jianjun Liu, Duihui Xiang
Rational normal form is a powerful tool to deal with Hamiltonian partial differential equations without external parameters. In this paper, we build rational normal form with exact…
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…
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…
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…
Stability of KAM tori for nonlinear Schrodinger equation
Cong Hongzi, Liu Jianjun, Yuan Xiaoping
It is proved that the KAM tori (thus quasi-periodic solutions) are long time stable for nonlinear Schrodinger equation.
Long time stability of KAM tori for nonlinear wave equation
Cong Hongzi, Gao Meina, Liu Jianjun
It is proved that the KAM tori (thus quasi-periodic solutions) are long time stable for infinite dimensional Hamiltonian systems generated by nonlinear wave equation, by constructi…