6 citations · 6 across the 10 of their papers we have counts for
12 papers
Logarithmic concentration for the focusing cubic Schrödinger equation on the two-dimensional torus
Xi Chen
We construct a smooth solution of the focusing cubic nonlinear Schrödinger equation on a square two-dimensional torus which is global in both time directions and concentrates at on…
Infinite cascades for the defocusing cubic half-wave equation on the torus
Xi Chen
We construct global solutions of the defocusing cubic half-wave equation on the torus whose norms grow exponentially for every . Such solutions exist at every posi…
Infinite cascades for the cubic nonlinear half-wave equation on the line
Xi Chen
We construct infinite-time Sobolev cascades for the cubic nonlinear half-wave equation on the real line. For and , spatial gluing of perman…
Talbot effect for the periodic Benjamin--Ono equation
Xi Chen
We study the dependence on time of the spatial regularity of solutions to the periodic Benjamin--Ono equation with real, mean-zero initial data of bounded variation. For every datu…
Failure of fixed-profile modified scattering and generalized modified scattering for the 1D defocusing cubic NLS
Xi Chen
We study the long-time behavior of the one-dimensional defocusing cubic nonlinear Schrödinger equation with initial data in . We first prove that the standard fixed…
The Calderón Problem for Quasilinear Conductivities of Conformally Transversally Anisotropic Media
Xi Chen, Ziyun Jin
This paper investigates Calderón's problem on a conformally transversally anisotropic manifold of dimension , where the conductivity might depend o…
Scattering of the defocusing Calogero--Moser derivative nonlinear Schrödinger equation
Xi Chen
In this paper, we study the long time behavior of solutions to the defocusing Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS). Using the Gérard-type explicit fo…
Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds
Tianyu Cai, Xi Chen
This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schrödinger equations with drift on connected closed Riemannian manifolds. We prov…
An inverse problem for the Standard Model of particle physics
Xi Chen, Matti Lassas, Lauri Oksanen +1
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the rep…
The defocusing Calogero--Moser derivative nonlinear Schr{ö}dinger equation with a nonvanishing condition at infinity
Xi Chen
We consider the defocusing Calogero--Moser derivative nonlinear Schr{ö}dinger equation\begin{align*}i \partial_{t} u+\partial_{x}^2 u-2ΠD\left(|u|^{2}\right)u=0, \quad (t,x ) \in \…
Spectrally accurate fully discrete schemes for some nonlocal and nonlinear integrable PDEs via explicit formulas
Yvonne Alama Bronsard, Xi Chen, Matthieu Dolbeault
We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szegő equations on the torus, which are with $\textit{spectra…
Explicit formula for the Benjamin--Ono equation with square integrable and real valued initial data and applications to the zero dispersion limit
Xi Chen
In this paper, we extend G{é}rard's formula for the solution of the Benjamin--Ono equation on the line to square integrable and real valued initial data. Combined with this formula…