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Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures (1610.08542v3)
Published 26 Oct 2016 in math-ph, math.AP, and math.MP
Abstract: We consider a nonlinear Schroedinger 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.
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