6 papers
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 b…
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 b…
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…
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 unboun…
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…