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

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journal contribution
posted on 23.03.2021, 18:39 by J Arbunich, C Sparber
© 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.

Funding

CAREER: Adiabatic theory for nonlinear Schrodinger equations with applications in complex quantum systems

Directorate for Mathematical & Physical Sciences

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History

Citation

Arbunich, J.Sparber, C. (2018). Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures. Journal of Mathematical Physics, 59(1), 011509-. https://doi.org/10.1063/1.5021754

Publisher

AIP Publishing

Language

en

issn

0022-2488