@Article{JMS-53-2,
author = {Yongyong, Cai and Yan, Wang},
title = {(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations},
journal = {Journal of Mathematical Study},
year = {2020},
volume = {53},
number = {2},
pages = {125--142},
abstract = {<p style="text-align: justify;">We consider&nbsp; 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 &#39;free Dirac operator&#39; 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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v53n2.20.01},
url = {https://global-sci.com/article/87694/semi-nonrelativisitic-limit-of-the-nonlinear-dirac-equations}
}