5 papers · 1 filter
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…
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…
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…
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…