6 papers
The Existence of full dimensional tori for d-dimensional Nonlinear Schr$\ddot{\mbox{O}}$dinger equation
Hongzi Cong, Xiaoqing Wu, Yuan Wu
In this paper, we prove the existence of full dimensional tori for -dimensional nonlinear Schr$\ddot{\mbox{o}}$dinger equation with periodic boundary conditions \begin{equation*…
The Existence of Full Dimensional KAM tori for Nonlinear Schrödinger equation
Hongzi Cong
In this paper, we will prove the existence of full dimensional tori for 1-dimensional nonlinear Schrödinger equation with periodic boundary conditions \begin{equation*}\label{L1} \…
Long-time Anderson Localization for the Nonlinear Schrodinger Equation Revisited
Hongzi Cong, Yunfeng Shi, Zhifei Zhang
In this paper, we confirm the conjecture of Wang and Zhang (J. Stat. Phys. 134 (5-6): 953--968, 2009) in a long time scale, i.e., the displacement of the wavefront for nonline…
The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation
Hongzi Cong, Xiaoping Yuan
In this paper we prove the existence and linear stability of full dimensional tori with subexponential decay for 1-dimensional nonlinear wave equation with external parameters, whi…
On the existence of full dimensional KAM torus for nonlinear Schrödinger equation
Hongzi Cong, Lufang Mi, Yunfeng Shi +1
In this paper, we study the following nonlinear Schrödinger equation \begin{eqnarray}\label{maineq0} \textbf{i}u_{t}-u_{xx}+V*u+εf(x)|u|^4u=0,\ x\in\mathbb{T}=\mathbb{R}/2π\mathbb{…
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…