18 citations · 71 across the 16 of their papers we have counts for
16 papers
Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domains
Emmanuel E. Oguadimma, Victory C. Obieke, Xueying Yu
We consider the cubic nonlinear Schrödinger (NLS) equation on two-dimensional flat tori with varying aspect ratios. In this formulation, the choice of aspect ratio governs the Four…
On Strichartz estimates for many-body Schrödinger equation in the periodic setting
Xiaoqi Huang, Xueying Yu, Zehua Zhao +1
In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori , where . The results hold for…
On recovering the nonlinearity for generalized higher-order Schrödinger equations
Zachary Lee, Xueying Yu
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schrödinger equations to higher-order Schrödinger equations with a more general no…
On well-posedness results for the cubic-quintic NLS on
Yongming Luo, Xueying Yu, Haitian Yue +1
We consider the periodic cubic-quintic nonlinear Schrödinger equation \begin{align}\label{cqnls_abstract} (i\partial_t +Δ)u=μ_1 |u|^2 u+μ_2 |u|^4 u\tag{CQNLS} \end{align} on the th…
On the uniqueness of variable coefficient Schrödinger equations
Serena Federico, Zongyuan Li, Xueying Yu
We prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coeffi…
Modified Scattering of Cubic Nonlinear Schrödinger Equation on Rescaled Waveguide Manifolds
Bobby Wilson, Xueying Yu
We use modified scattering theory to demonstrate that small-data solutions to the cubic nonlinear Schrödinger equation on rescaled waveguide manifolds, $\mathbb{R} \times \mathbb{T…
Singular Levy processes and dispersive effects of generalized Schrödinger equations
Yannick Sire, Xueying Yu, Haitian Yue +1
We introduce new models for Schrödinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to under…
On the decay property of the cubic fourth-order Schrödinger equation
Xueying Yu, Haitian Yue, Zehua Zhao
In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on () enjoys the same (pointwise) decay proper…
Global Well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds
Xueying Yu, Haitian Yue, Zehua Zhao
In this paper, we study the well-posedness theory and the scattering asymptotics for fourth-order Schrödinger equations (4NLS) on waveguide manifolds (semiperiodic spaces) $\mathbb…
On the global well-posedness for the periodic quintic nonlinear Schrödinger equation
Xueying Yu, Haitian Yue
In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on with general data in the critical Sobolev space $H^{\f…
Global well-posedness and long-time behavior of the fractional NLS
Mouhamadou Sy, Xueying Yu
In this paper, our discussion mainly focuses on equations with energy supercritical nonlinearities. We establish probabilistic global well-posedness (GWP) results for the cubic Sch…
Global well-posedness for the cubic fractional NLS on the unit disk
Mouhamadou Sy, Xueying Yu
In this paper, we prove that the cubic nonlinear Schrödinger equation with the fractional Laplacian on the unit disk is globally well-posed for certain radial initial data below th…
Global Well-posedness for the focusing cubic NLS on the product space
Xueying Yu, Haitian Yue, Zehua Zhao
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space with initial data bel…
Almost sure global well-posedness for the energy supercritical NLS on the unit ball of
Mouhamadou Sy, Xueying Yu
In this paper, we present two almost sure global well-posedness (GWP) results for the energy supercritical nonlinear Schrödinger equations (NLS) on the unit ball of usin…
On the high-low method for NLS on the hyperbolic space
Gigliola Staffilani, Xueying Yu
In this paper, we first prove that the cubic, defocusing nonlinear Schrödinger equation on the two dimensional hyperbolic space with radial initial data in is g…
Global well-posedness and scattering for the defocusing -critical nonlinear Schrödinger equation in
Xueying Yu
In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in with general data in the critical space $\dot…