Nonlinear Dirac equation for graphene

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.