4 papers · 1 filter
A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications
Yuan Wu, Xiaoping Yuan
In this paper, we investigate the existence of KAM tori for an infinite dimensional Hamiltonian system with finite number of zero normal frequencies. By constructing a constant qua…
Krylov--Bogolyubov averaging
Wenwen Jian, Sergei Kuksin, Yuan Wu
We present the modified approach to the classical Bogolyubov-Krylov averaging, developed recently for the purpose of PDEs. It allows to treat Lipschitz perturbations of linear syst…
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{…
On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range
Yuan Wu, Xiaoping Yuan
In this paper, it is proved that the infinite KAM torus with prescribed frequency exists in a sufficiently small neighborhood of a given for nearly integrable and analytic…