High-order conservative schemes for the nonlinear Dirac equation

DOI10.1080/00207160.2019.1698735OpenAlexW2991565976WikidataQ126658190 ScholiaQ126658190MaRDI QIDQ5031173

Shu-Cun Li, Xiang-Gui Li

Publication date: 18 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2019.1698735

zbMATH Keywords

dynamicsnonlinear Dirac equationhigh-order conservative schemeoperator-compensation

Mathematics Subject Classification ID

Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Computational methods for problems pertaining to quantum theory (81-08) Numerical analysis (65-XX)

Related Items (1)

Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction

Cites Work

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• A numerical study of the ground state and dynamics of atomic-molecular Bose-Einstein condensates
• Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• Numerical methods for nonlinear Dirac equation
• A combined discontinuous Galerkin method for the dipolar Bose-Einstein condensation
• Nonlinear spinor fields and its role in cosmology
• The finite element method for computing the ground states of the dipolar Bose-Einstein condensates
• Multi-hump solitary waves of a nonlinear Dirac equation
• The numerical study of a nonlinear one-dimensional Dirac equation
• A soluble relativistic field theory
• An efficient adaptive mesh redistribution method for a nonlinear Dirac equation
• Existence of stationary states for nonlinear Dirac equations
• Interaction for the solitary waves of a nonlinear Dirac model
• A numerical method with particle conservation for the Maxwell-Dirac system
• Existence of localized solutions for a classical nonlinear Dirac field
• Split-step spectral schemes for nonlinear Dirac systems
• Linearized Crank-Nicolson scheme for nonlinear Dirac equations
• Numerical methods for the derivative nonlinear Schrödinger equation
• Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D
• High-order compact methods for the nonlinear Dirac equation
• An efficient and stable numerical method for the Maxwell--Dirac system
• Stationary states of the nonlinear Dirac equation: A variational approach
• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• A time-splitting spectral scheme for the Maxwell-Dirac system
• Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model
• Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
• Nonlinear Spinor Field
• Quantum Theory of Fields and Elementary Particles
• A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime
• The nonlinear Dirac equation in Bose–Einstein condensates: superfluid fluctuations and emergent theories from relativistic linear stability equations
• Time‐splitting methods with charge conservation for the nonlinear Dirac equation
• On the Construction and Comparison of Difference Schemes
• Nonlinear Spinor Fields

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