8 papers
Nonlocal modeling of opinion alignment and environmental feedback: Spatial aggregation and non-consensus patterns
Rui Wang, Yunfeng Xiong, Zhengru Zhang +1
The formation of public opinion in modern information environments is shaped by the interplay between social conformity and information exposure. While social interactions promote…
Numerical solution of the nonlinear Dirac equation by a splitting variational quantum algorithm
Qian Zuo, Ying He, Xiaofei Zhao
In this work, we propose an operator-splitting variational quantum algorithm, termed Dirac-sVQA, for simulating the nonlinear Dirac equation (NLDE). The main difficulty arises from…
Analysis of gradient flow for computing defocusing action ground states of rotating nonlinear Schrödinger equations
Wei Liu, Tingfeng Wang, Yongjun Yuan +1
This work focuses on the numerical computation of defocusing action ground states for rotating nonlinear Schrödinger equations (RNLS) using a direct gradient flow (DGF) method. We…
Quasi-Monte Carlo time-splitting methods for the Schrödinger equation with Gaussian random potential
Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao
In this paper, we study the Schrödinger equation with a Gaussian random potential (SE-GP) and develop an efficient numerical method to approximate the expectation of physical obser…
Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data
Lun Ji, Xiaofei Zhao
In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein--Gordon/wave equation under rough initial data. The optimal error bounds of the…
The cubic nonlinear Schrödinger equation with rough potential
Norbert J. Mauser, Yifei Wu, Xiaofei Zhao
We consider the cubic nonlinear Schrödinger equation with a spatially rough potential, a key equation in the mathematical setup for nonlinear Anderson localization. Our study compr…
Error estimate of a quasi-Monte Carlo time-splitting pseudospectral method for nonlinear Schrodinger equation with random potentials
Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao
In this paper, we consider the numerical solution of a nonlinear Schrodinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combi…
A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime
Weizhu Bao, Yongyong Cai, Xiaofei Zhao
We propose and analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for solving the Klein-Gordon (KG) equation with a dimensionless parameter $0<\varepsilon\…