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 Matem. Mod., 2020, Volume 32, Number 8, Pages 43–56 (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)

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_à

DOI: https://doi.org/10.20948/mm-2020-08-04

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Revised: 05.09.2019
Accepted:21.10.2019

Citation: A. A. Gladkikh, G. G. Malinetskii, “Nonlinear Dirac equation for graphene”, Matem. Mod., 32:8 (2020), 43–56

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}