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Matematicheskoe modelirovanie, 2020, Volume 32, Number 8, Pages 43–56
DOI: https://doi.org/10.20948/mm-2020-08-04 (Mi mm4205) 		 
Nonlinear Dirac equation for graphene

A. A. Gladkikhab, G. G. Malinetskiiab

a Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)
b Moscow Intitute of Physics and Technology (National Research University)
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DOI: https://doi.org/10.20948/mm-2020-08-04
Abstract: We consider a nonlinear Dirac equation in order to describe collective electronic phenomena. In comparison to the other papers on the given topic the interaction term includes the sum of the spinor components’ squares instead of their difference. We investigate the properties of the obtained nonlinear equation, pretending to describe hightemperature ferromgnetism without assumptions about the key role of defects. The numerical simulation was done for simple boundary and initial conditions with Lax–Friedrichs scheme.
Keywords: nonlinear Dirac equation, graphene, numerical simulation.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00602_а
Received: 05.09.2019
Revised: 05.09.2019
Accepted: 21.10.2019
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 2, Pages 301–310
DOI: https://doi.org/10.1134/S2070048221020083
Document Type: Article
Language: Russian
Citation: A. A. Gladkikh, G. G. Malinetskii, “Nonlinear Dirac equation for graphene”, Matem. Mod., 32:8 (2020), 43–56; Math. Models Comput. Simul., 13:2 (2021), 301–310
Citation in format AMSBIB
\Bibitem{GlaMal20}
\by A.~A.~Gladkikh, G.~G.~Malinetskii
\paper Nonlinear Dirac equation for graphene
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 8
\pages 43--56
\mathnet{http://mi.mathnet.ru/mm4205}
\crossref{https://doi.org/10.20948/mm-2020-08-04}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 2
\pages 301--310
\crossref{https://doi.org/10.1134/S2070048221020083}
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    		Математическое моделирование
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