Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures

© 2018 Author(s). We consider a nonlinear Schrödinger equation in two spatial dimensions subject to a periodic honeycomb lattice potential. Using a multi-scale expansion together with rigorous error estimates, we derive an effective model of nonlinear Dirac type. The latter describes the propagation of slowly modulated, weakly nonlinear waves spectrally localized near a Dirac point.