8 papers
A Parameterization of Small Amplitude KP Finite Gap Solutions via Classical Schottky Uniformization and Persistence of One and Two Gap Solutions
Haoxuan Liu, Zuhong You, Xiaoping Yuan
We develop a parameterization of small amplitude finite gap solutions to the KP equation with prescribed spatial wavenumber vectors using classical Schottky uniformization. This pa…
On the construction of almost periodic solutions for the derivative nonlinear Schrödinger equation
Yuchen WU, Xiaoping Yuan
In this paper, we consider a derivative nonlinear Schrödinger equation on the torus $…
Anderson localization for 1-d quasi-periodic Schrödinger operators with degenerate weights
Yingdu Dong, Haoxuan Liu, Zuhong You +1
We establish Anderson localization for 1-d discrete Schrödinger operators with positive weights. The distinctive feature of this work lies in the degeneracy of the weights, with bo…
Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schrödinger Equations via Resonant Mode Control
Zuhong You, Xiaoping Yuan
This paper focuses on the problem of quasi-periodic solutions for multi-dimensional quasi-linear Schrödinger equation. To address the challenge of unbounded perturbations caused by…
Periodic Response Solutions to Multi-Dimensional Nonlinear Schrödinger equation with unbounded perturbation
Zuhong You, Xiaoping Yuan
By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of periodic response solutions to multi-dimensional nonlinear Schrödinger equations (NLS) with unbound…
Construction of periodic solutions of multi-dimensional nonlinear wave equations with unbounded perturbation
Huining Xue, Zuhong You, Xiaoping Yuan
By applying the Craig-Wayne-Bourgain (CWB) method, we establish the persistence of periodic solutions to multi-dimensional nonlinear wave equations (NLW) with unbounded perturbatio…
Construction of Quasi-periodic solutions with the same Gevrey index as nonlinear terms in Multi-Dimensional NLS
Zuhong You, Xiaoping Yuan
We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schrödinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey…
Long time stability for KAM tori of the derivative nonlinear Schrödinger equation
Shengqing Hu, Huining Xue, Xiaoping Yuan
This paper is concerned with the long time stability of KAM tori for a class of derivative nonlinear Schrödinger equations subjected to periodic boundary condition.