Dispersion analysis of multi-symplectic scheme for the nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: Dispersion analysis of multi-symplectic scheme for the nonlinear Schrödinger equations
zbMATH Open document ID: 1483.65139
author: Haochen Li
author: Hang Ye
author: Xue-jun He
author: Jianqiang Sun
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2020-04-15T00:00:00Z
review text: Dispersive properties of multi-symplectic discretizations for the nonlinear Schrödinger (NLS) equations are investigated. Numerical dispersion relations and group velocities are derived for the single and coupled (NLS) equations depending on the space \(\Delta x\) and time \(\Delta t\) mesh sizes. These are confirmed by numerical results for the NLS equations.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 65P10
zbMATH DE Number: 7189540
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: multi-symplectic scheme
zbMATH Keywords: dispersion analysis
zbMATH Keywords: group velocity
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
full work available at URL: s10255-020-0933-4
OpenAlex ID: W3016197470
cites work: HAMILTONIAN INTEGRATORS FOR THE NONLINEAR SCHROEDINGER EQUATION
cites work: Multisymplectic box schemes and the Korteweg-de Vries equation.
cites work: Multisymplectic box schemes for the complex modified Korteweg–de Vries equation
cites work: Model equations for long waves in nonlinear dispersive systems
cites work: Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
cites work: Numerical methods for Hamiltonian PDEs
cites work: Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
cites work: Numerical dispersion analysis of a multi-symplectic scheme for the three dimensional Maxwell's equations
cites work: Q4433568
cites work: Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
cites work: Symplectic Geometric Algorithms for Hamiltonian Systems
cites work: Linear PDEs and Numerical Methods That Preserve a Multisymplectic Conservation Law
cites work: Multisymplecticity of the centred box scheme for a class of Hamiltonian PDEs and an application to quasi-periodically solitary waves
cites work: The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
cites work: Q3052264
cites work: Splitting multisymplectic integrators for Maxwell's equations
cites work: Backward error analysis for multi-symplectic integration methods
cites work: Multisymplectic geometry, variational integrators, and nonlinear PDEs
cites work: Backward Error Analysis for Numerical Integrators
cites work: Dispersive properties of multisymplectic integrators
cites work: Symplectic and multisymplectic numerical methods for Maxwell's equations
cites work: Q4151274
DOI: 10.1007/S10255-020-0933-4
description: scientific article; zbMATH DE number 7189540