Xi Chen

activity

20242026

most citedExplicit formula for the Benjamin--Ono equation with square integrable and real valued initial data and applications to the zero dispersion limit

6 citations · 6 across the 10 of their papers we have counts for

collaborators

Showing 2026 · math.APShow all

5 papers · 2 filters

math.AP2026

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…

math.AP2026

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 $H^{s}$ norms grow exponentially for every $1/2 < s < 3/2$ . Such solutions exist at every posi…

math.AP2026

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 $\frac{1}{2} < s \leq 1$ and $0 \leq κ < 2 s (2 s - 1) / (4 s - 1)$ , spatial gluing of perman…

math.AP2026

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…

math.AP2026

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 $L^{2} (R)$ . We first prove that the standard fixed…