2 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…