Abstract
The Maxwell equations for an electromagnetic field propagating in graphene in which electrons with different spin projections experience a strong Coulomb repulsion at a single node are considered. An effective equation analogous to the classical (1+1)-dimensional sine-Gordon equation is derived. Electrons are treated within the framework of the quantum formalism with allowance for changes in the dispersion law in the presence of Coulomb interaction. The effective equation is solved numerically, and the effect of Coulomb repulsion is identified. The amplification of an ultrashort pulse is observed when an external uniform electromagnetic field with a period shorter than the pulse duration is applied.
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