Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations

DOI10.1007/s11425-013-4575-3zbMath1264.65144OpenAlexW2270657159MaRDI QIDQ1955490

Lan Wang, Shanshan Jiang, Linghua Kong, Ya-Li Duan

Publication date: 11 June 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-013-4575-3

zbMATH Keywords

conservation lawsolitonKlein-Gordon-Schrödinger equationsFourier pseudo-spectral methodmultisymplectic integrator

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (18)

Superconvergence Analysis of a BDF-Galerkin FEM for the Nonlinear Klein-Gordon-Schr\"{o}dinger Equations with Damping Mechanism ⋮ General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs ⋮ Symplectic‐preserving Fourier spectral scheme for space fractional<scp>Klein–Gordon–Schrödinger</scp>equations ⋮ Conservative Fourier spectral scheme for higher order Klein-Gordon-Schrödinger equations ⋮ An efficient conservative difference scheme for fractional Klein-Gordon-Schrödinger equations ⋮ Improved uniform error bounds of a time-splitting Fourier pseudo-spectral scheme for the Klein-Gordon-Schrödinger equation with the small coupling constant ⋮ An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations ⋮ A Fourier spectral method for the nonlinear coupled space fractional Klein‐Gordon‐Schrödinger equations ⋮ Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation ⋮ Unconditional error estimates of linearized BDF2-Galerkin FEMs for nonlinear coupled Schrödinger-Helmholtz equations ⋮ Analysis of a Fourier pseudo-spectral conservative scheme for the Klein–Gordon–Schrödinger equation ⋮ Analysis of a conservative high-order compact finite difference scheme for the Klein-Gordon-Schrödinger equation ⋮ Optimal error estimate of a linear Fourier pseudo-spectral scheme for two dimensional Klein-Gordon-Schrödinger equations ⋮ Multi-symplectic preserving integrator for the Schrödinger equation with wave operator ⋮ Unconditional optimal error estimates of conservative methods for Klein-Gordon-Dirac system in two dimensions ⋮ Meshless symplectic and multi-symplectic algorithm for Klein-Gordon-Schrödinger system with local RBF collocation ⋮ The Multisymplectic Diamond Scheme ⋮ Conservative Fourier pseudo-spectral schemes for general Klein–Gordon–Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• On the preservation of phase space structure under multisymplectic discretization
• Numerical simulation of interaction between Schrödinger field and Klein-Gordon field by multisymplectic method
• Splitting multisymplectic integrators for Maxwell's equations
• Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations
• On coupled Klein-Gordon-Schrödinger equations. II
• The periodic wave solutions for the Klein-Gordon-Schrödinger equations
• Convergence of a conservative difference scheme for a class of Klein-Gordon-Schrödinger equations in one space dimension
• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• Quadratic invariants and multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
• Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations
• Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
• Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation

This page was built for publication: Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations