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math.AP2026
Scattering in spacetime cones for the nonlinear Schrödinger equation
Andrew Hassell, Qiuye Jia, Xiaoxu Wu
We consider the nonlinear Schrödinger equation on , with a class of `mixed' nonlinearities that admit soliton solutions. We are interested in the long-time behavi…
math.AP2026
Long-range scattering
Avy Soffer, Gavin Stewart, Xiaoxu Wu
We study the scattering problem for a long range potential, which is time dependent. We prove the existence and completeness of the scattering wave operators, and find some propert…
math.AP2026
Local-in-Time Existence of solutions to the Gravity Water Wave Kinetic Equation
Yulin Pan, Xiaoxu Wu
In this paper, we study the Cauchy problem for the four-wave kinetic equation describing the weak turbulence of gravity water waves. The mathematical challenges of this analysis st…