8 citations · 8 across the 3 of their papers we have counts for
3 papers
math.DS2019
A KAM Theorem for Two-dimensional Nonlinear Schrödinger Equations
Jiansheng Geng, Shuaishuai Xue
We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the two-dimensional nonlinear Schrödinger equation $$iu_t-\triangle u +|u|^2u+\frac{\pa…
math.DS2019
A KAM Theorem for Higher Dimensional Reversible Nonlinear Schrödinger Equations
Yingnan Sun, Zhaowei Lou, Jiansheng Geng
In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear sta…
math.DS2017★ 8 cited
An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation
Jiansheng Geng, Shidi Zhou
In this paper we consider the completely resonant beam equation on \T^2 with cubic nonlinearity on a subspace of L^2 (\T^2) which will be explained later. We establish an abstract…