Close Search Advanced
Journals
Resources
About Us
Open Access

(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations

(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations
Preview
Add to basket

Year:    2020

Author:    Yongyong Cai, Yan Wang

Journal of Mathematical Study, Vol. 53 (2020), Iss. 2 : pp. 125–142

Abstract

We consider  the nonlinear Dirac equation (NLD) with time dependent external electro-magnetic potentials, involving a dimensionless parameter $ε\in(0,1]$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime $ε\ll1$ (speed of light tends to infinity), we decompose the solution into the eigenspaces associated with the 'free Dirac operator' and construct an approximation to the NLD with $O(ε^2)$ error. The NLD converges (with a phase factor) to a coupled nonlinear Schrödinger system (NLS) with external electric potential in the nonrelativistic limit as $ε\to0^+$, and the error of the NLS approximation is first order $O(ε)$. The constructed $O(ε^2)$ approximation is well-suited for numerical purposes.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v53n2.20.01

Journal of Mathematical Study, Vol. 53 (2020), Iss. 2 : pp. 125–142

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Nonlinear Dirac equation nonrelativistic limit error estimates.

Author Details

Yongyong Cai

Yan Wang

  1. Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime

    Cai, Yongyong | Wang, Yan

    Multiscale Modeling & Simulation, Vol. 20 (2022), Iss. 1 P.164

    https://doi.org/10.1137/20M133573X [Citations: 2]

  2. A uniformly accurate method for the Klein-Gordon-Dirac system in the nonrelativistic regime

    Cai, Yongyong | Yi, Wenfan

    Journal of Computational Physics, Vol. 486 (2023), Iss. P.112105

    https://doi.org/10.1016/j.jcp.2023.112105 [Citations: 1]

  3. On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation

    Jahnke, Tobias | Kirn, Michael

    BIT Numerical Mathematics, Vol. 63 (2023), Iss. 2

    https://doi.org/10.1007/s10543-023-00971-1 [Citations: 0]

  4. Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential

    Bao, Weizhu | Cai, Yongyong | Yin, Jia

    SIAM Journal on Numerical Analysis, Vol. 59 (2021), Iss. 2 P.1040

    https://doi.org/10.1137/19M1271828 [Citations: 10]