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math.DS2019
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…
math.DS2019
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…
math.DS2019
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{…