54 citations · 225 across the 20 of their papers we have counts for
21 papers
Some uniform error analysis for gKdV equations in dispersionless limit regime before dispersive shock
Bing Li, Tingfeng Wang, Xiaofei Zhao
This work establishes uniform error estimates for classical numerical schemes applied to the generalized Korteweg-de Vries (gKdV) equation in the dispersionless limit regime, speci…
Computing the action ground state for the rotating nonlinear Schrödinger equation
Wei Liu, Yongjun Yuan, Xiaofei Zhao
We consider the computations of the action ground state for a rotating nonlinear Schrödinger equation. It reads as a minimization of the action functional under the Nehari constrai…
Geometric two-scale integrators for highly oscillatory system: uniform accuracy and near conservations
Bin Wang, Xiaofei Zhao
In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter . The problem arises from many physical models i…
Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes
Xavier Antoine, Xiaofei Zhao
Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon e…
Embedded exponential-type low-regularity integrators for KdV equation under rough data
Yifei Wu, Xiaofei Zhao
In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal convergence resul…
Numerical integrators for continuous disordered nonlinear Schrödinger equation
Xiaofei Zhao
In this paper, we consider the numerical solution of the continuous disordered nonlinear Schrödinger equation, which contains a spatial random potential. We address the finite time…
Error estimates of some splitting schemes for charged-particle dynamics under strong magnetic field
Bin Wang, Xiaofei Zhao
In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving…
Optimal convergence of a second order low-regularity integrator for the KdV equation
Yifei Wu, Xiaofei Zhao
In this paper, we establish the optimal convergence result of a second order exponential-type integrator from (136, Numer. Math., 2017) for solving the KdV equation under rough ini…
Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction
Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou +2
In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous, varying direction, strong magnetic field. Whenever the magnetic field has constant intensity…
Low-regularity integrators for nonlinear Dirac equations
Katharina Schratz, Yan Wang, Xiaofei Zhao
In this work, we consider the numerical integration of the nonlinear Dirac equation and the Dirac-Poisson system (NDEs) under rough initial data. We propose a ultra low-regularity…
A uniformly and optimally accurate method for the Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime
Chunmei Su, Xiaofei Zhao
We present a uniformly and optimally accurate numerical method for solving the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters and , which…
Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
Weizhu Bao
Different efficient and accurate numerical methods have recently been proposed and analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter $\varepsil…
Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field
Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou +2
In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent un…
Symmetric high order Gautschi-type exponential wave integrators pseudospectral method for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
Yan Wang, Xiaofei Zhao
A group of high order Gautschi-type exponential wave integrators (EWIs) Fourier pseudospectral method are proposed and analyzed for solving the nonlinear Klein-Gordon equation (KGE…
Modulation equations approach for solving vortex and radiation in nonlinear Schrodinger equation
Avy Soffer, Xiaofei Zhao
We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schrödinger equation. The full modulation equations which describe the dy…
Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime
Mohammed Lemou, Florian Méhats, Xiaofei Zhao
We apply the two-scale formulation approach to propose uniformly accurate (UA) schemes for solving the nonlinear Dirac equation in the nonrelativistic limit regime. The nonlinear D…
A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS
Avy Soffer, Xiaofei Zhao
Based on our previous work for solving the nonlinear Schrodinger equation with multichannel dynamics that is given by a localized standing wave and radiation, in this work we deal…
A uniformly accurate (UA) multiscale time integrator Fourier pseoduspectral method for the Klein-Gordon-Schrodinger equations in the nonrelativistic limit regime
Weizhu Bao, Xiaofei Zhao
A multiscale time integrator Fourier pseudospectral (MTI-FP) method is proposed and analyzed for solving the Klein-Gordon-Schrödinger (KGS) equations in the nonrelativistic limit r…
On multichannel solutions of nonlinear Schrödinger equations: algorithm, analysis and numerical explorations
Avy Soffer, Xiaofei Zhao
We apply the method of modulation equations to numerically solve the NLS with multichannel dynamics, given by a trapped localized state and radiation. This approach employs the mod…
Scalar-field theory of dark matter
Kerson Huang, Chi Xiong, Xiaofei Zhao
We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the su…
Uniformly accurate multiscale time integrators for highly oscillatory second order differential equations
Weizhu Bao, Xuanchun Dong, Xiaofei Zhao
In this paper, two multiscale time integrators (MTIs), motivated from two types of multiscale decomposition by either frequency or frequency and amplitude, are proposed and analyze…