13 citations · 19 across the 14 of their papers we have counts for
14 papers
The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions
Hongzi Cong, Wanran Ding, Zhihan Zhang +1
We prove the existence of full dimensional KAM tori for infinite dimensional mechanical systems exhibiting long range interactions, under a Diophantine condition of Bourgain type […
The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation
Hongzi Cong, Siming Li, Xiaoqing Wu
In this paper, we investigate the almost-periodic solutions for the one-dimensional nonlinear Klein-Gordon equation within the non-relativistic limit under periodic boundary condit…
Long-time Anderson Localization for the Nonlinear quasi-periodic Schrödinger Equation on
Hongzi Cong, Yunfeng Shi, W. -M. Wang
Using a Birkhoff normal form transform to impede mode transfer in a finite "barrier", we prove localization of arbitrary data for polynomially long time for the nonlinear…
Localization for random coupled harmonic oscillators on
Hongzi Cong, Yunfeng Shi, Zhihan Zhang
In this paper we consider the localization properties of coupled harmonic oscillators in random media. Each of these oscillators is restricted to the lattice . We sho…
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} \…
Diffusion bound for the nonlinear Anderson model
Hongzi Cong, Yunfeng Shi
In this paper, we prove the power-law in time upper bound for the diffusion of a 1D discrete nonlinear Anderson model. We remove completely the decaying condition restricted on the…
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…
Stickiness of KAM tori for higher dimensional beam equation
Xiucui Song, Hongzi Cong
This paper is concerned with the stickiness of invariant tori obtained by KAM technics (so-called KAM tori) for higher dimensional beam equation. We prove that the KAM tori are sti…
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…