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.
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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.