8 papers
Talbot effect for the periodic Benjamin--Ono equation
Xi Chen
We study the Talbot effect for the periodic Benjamin--Ono equation with rough initial data. Using the smoothing theorem of Gérard--Kappeler--Topalov for Tao's gauge transform, we…
Failure of Fixed-Profile Modified Scattering at the Pure Endpoint for the 1D Defocusing Cubic NLS
Xi Chen
We prove that the standard fixed-profile modified-scattering ansatz fails at the unweighted endpoint for the one-dimensional defocusing cubic nonlinear Schrödinger equation.…
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…
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…
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 pro…
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 SzegÅ equations on the torus, which are with $\textit{spectr…