Jiansheng Geng | Researchain

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Nonlinearity | 2007

A KAM theorem for Hamiltonian networks with long ranged couplings

Jiansheng Geng; Yingfei Yi

We consider Hamiltonian networks of long-ranged and weakly coupled oscillators with variable frequencies. By deriving an abstract infinite dimensional KAM type of theorem, we show that for any given positive integer N and a fixed, positive measure set of N variable frequencies, there is a subset of positive measure such that each corresponds to a small amplitude, quasi-periodic breather (i.e. a solution which is quasi-periodic in time and exponentially localized in space) of the Hamiltonian network with N-frequencies which are slightly deformed from ω.

Siam Journal on Mathematical Analysis | 2013

Quasi-periodic Solutions for One-Dimensional Nonlinear Lattice Schrödinger Equation with Tangent Potential

Jiansheng Geng; Zhiyan Zhao

In this paper, we construct time quasi-periodic solutions for the nonlinear lattice Schrodinger equation

Communications in Mathematical Physics | 2006

A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces

Jiansheng Geng; Jiangong You

{\rm i}\dot{q}_n+\epsilon (q_{n+1}+q_{n-1}) +\tan\pi(n\tilde{\alpha}+x)q_n+\epsilon|q_n|^2q_n=0

Journal of Differential Equations | 2005

A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions

Jiansheng Geng; Jiangong You

Journal of Differential Equations | 2007

Quasi-Periodic Solutions in a Nonlinear Schrödinger Equation

Jiansheng Geng; Yingfei Yi

n\in\mathbb{Z},

Advances in Mathematics | 2011

An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation

Jiansheng Geng; Xindong Xu; Jiangong You

where

Nonlinearity | 2006

KAM tori for higher dimensional beam equations with constant potentials

Jiansheng Geng; Jiangong You

\tilde{\alpha}

Journal of Mathematical Analysis and Applications | 2003

KAM tori of Hamiltonian perturbations of 1D linear beam equations

Jiansheng Geng; Jiangong You

satisfies a certain Diophantine condition and

Nonlinearity | 2007

Almost periodic solutions for a class of higher-dimensional beam equations

Huawei Niu; Jiansheng Geng

x\in\mathbb{R}/\mathbb{Z}

Journal of Differential Equations | 2012

Invariant tori of full dimension for a nonlinear Schrödinger equation

Jiansheng Geng

. We prove that for

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