3 papers
math.PR2026
Large Deviations for the Nonlinear Schrödinger Equation with Randomized Quasi-Periodic Initial Data in Higher Dimensions: Subcritical Case
Fei Xu, Yong Li
We study the cubic weakly nonlinear Schrödinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier…
math.AP2024
Existence, Uniqueness and Asymptotic Dynamics of Nonlinear Schrödinger Equations With Quasi-Periodic Initial Data: II. The Derivative NLS
David Damanik, Yong Li, Fei Xu
This is the second part of a two-paper series studying the nonlinear Schrödinger equation with quasi-periodic initial data. In this paper, we focus on the quasi-periodic Cauchy pro…
math.AP2024
Existence, Uniqueness and Asymptotic Dynamics of Nonlinear Schrödinger Equations With Quasi-Periodic Initial Data: I. The Standard NLS
David Damanik, Yong Li, Fei Xu
This is the first part of a two-paper series studying nonlinear Schrödinger equations with quasi-periodic initial data. In this paper, we consider the standard nonlinear Schrödinge…