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∈(0,1] which is inversely proportional to the speed of light. In the nonrelativistic limit regime ε≪1 (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(ε2) 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→0+, and the error of the NLS approximation is first order O(ε). The constructed O(ε2) 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.
Author Details
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