2 citations · 6 across the 15 of their papers we have counts for
16 papers
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…
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…
Trotterization with Many-body Coulomb Interactions: Convergence for General Initial Conditions and State-Dependent Improvements
Di Fang, Xiaoxu Wu
Efficiently simulating many-body quantum systems with Coulomb interactions is a fundamental question in quantum physics, quantum chemistry, and quantum computing, yet it presents u…
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…
On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
Di Fang, Xiaoxu Wu, Avy Soffer
Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales…
Decomposition of global solutions for a class of nonlinear wave equations
Georgios Mavrogiannis, Avy Soffer, Xiaoxu Wu
In the present paper we consider global solutions of a class of non-linear wave equations of the form \begin{equation*} \Box u= N(x,t,u)u, \end{equation*} where the nonlinearity~$…
The three-quasi-particle scattering problem: asymptotic completeness for short-range systems
Avy Soffer, Xiaoxu Wu
We develop an approach to scattering theory for generalized -body systems. In particular we consider a general class of three quasi-particle systems, for which we prove Asymptot…
Decomposition of global solutions of bi-laplacian Nonautonomous Schrödinger equations
Avy Soffer, Jiayan Wu, Xiaoxu Wu +1
We study the bi-Laplacian Schrödinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions…
Soliton resolution for nonlinear Schrödinger type equations in the radial case
Avy Soffer, Xiaoxu Wu
We consider the Schrödinger equation with a general interaction term, which is localized in space, for radially symmetric initial data in dimensions, . The interaction…
Local Decay Estimates
Avy Soffer, Xiaoxu Wu
We give a proof of Local Decay Estimates for Schrödinger type equations, which is based on the knowledge of Asymptotic Completeness (AC). This approach extends to time dependent po…
On the Existence of Self-Similar solutions for some Nonlinear Schrödinger equations
Avy Soffer, Xiaoxu Wu
We construct solutions of Schrödinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solut…
On The large Time Asymptotics of Klein-Gordon type equations with General Data
Avy Soffer, Xiaoxu Wu
We study the Klein-Gordon equation with general interaction terms, which may be linear or nonlinear, and space-time dependent. We initiate the study of such equations with large (n…
On The large Time Asymptotics of Schrödinger type equations with General Data
Avy Soffer, Xiaoxu Wu
For the Schrödinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global solutio…
Boundedness of the Scattering Wave Operators of Schrödinger Dynamics -- Part 2
Avy Soffer, Xiaoxu Wu
We give another proof of the boundedness of scattering wave operators, at the low frequency part of the data. The proof also allows the control of the commutator of multiplic…
L^p Boundedness of the Scattering Wave Operators of Schroedinger Dynamics with Time-dependent Potentials and applications
Avy Soffer, Xiaoxu Wu
This paper establishes the boundedness of wave operators for linear Schrödinger equations in with time-dependent potentials. The approach to the proof is based…
Compound Poisson Point Processes, Concentration and Oracle Inequalities
Huiming Zhang, Xiaoxu Wu
This note aims at presenting several new theoretical results for the compound Poisson point process, which follows the work of Zhang \emph{et al.} [Insurance~Math.~Econom.~59(2014)…