Abstract
The possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference. Particular attention is paid to the equality of the spatial coordinates. We investigate the properties of the obtained nonlinear equation, in order to describe the high-temperature ferromagnetism in graphene without making any assumptions on the key role of defects of the structure in providing the effect. The numerical simulation is carried out for the simple boundary and initial conditions with the Lax–Friedrichs scheme as a result of which information is obtained on the dynamics of the electron density for a number of the simplest initial and boundary conditions.
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