26 citations · 85 across the 32 of their papers we have counts for
32 papers
Almost-sure quenched KAM tori for cubic NLS with a spatial white-noise potential
Yingdu Dong, Wenwen Jian, Xiaoping Yuan
Let \[ A_ω=-\partial_x^2+ρ\dot B_x(ω), \qquad ρ\ne0, \] be the Dirichlet Schrödinger operator on with a spatial Gaussian white-noise potential, realized pathwise via quasi-…
High-energy asymptotics for finite-interval Schrödinger operators with Gaussian white-noise potential
Yingdu Dong, Wenwen Jian, Xiaoping Yuan
We study the one-dimensional Schrödinger operator on a fixed interval with Gaussian white-noise potential, \[ H_ω=-\frac{\dd^2}{\dd x^2}+ρ\dot B_x(ω), \] under Dirichlet boundary c…
Long time stability of KAM tori for the nonlinear Schrödinger equation
Xiaolong He, Jia Shi, Xiaoping Yuan
In this paper, we prove the long time stability of KAM tori for the nonlinear Schrödinger equation on the torus with arbitrary dimensions.
A note on stability of Eliasson-Kuksin's KAM tori for the nonlinear Schrödinger equation
Xiaolong He, Jia Shi, Xiaoping Yuan
Eliasson and Kuksin developed a KAM approach to study the persistence of the invariant tori for nonlinear Schrödinger equation on . In this note, we improve Eliasso…
KAM theorem with large perturbation and application to network of Duffing oscillators
Xiaoping Yuan, Lu Chen, Jing Li
We prove that there is an invariant torus with given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a larg…
On linear stability of KAM tori via the Craig-Wayne-Bourgain method
Xiaolong He, Jia Shi, Yunfeng Shi +1
In this paper, we prove the Melnikov's persistency theorem by combining the traditional Kolmogorov-Arnold-Moser (KAM) technique and the Craig-Wayne-Bourgain (CWB) method. The aim o…