Calculus of Variations and Geometric Measure Theory
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W. Borrelli - R. Carlone

Bifurcating standing waves for effective equations in gapped honeycomb structures

created by borrelli on 13 Jan 2021
modified on 11 Mar 2021



Inserted: 13 jan 2021
Last Updated: 11 mar 2021

Journal: Nanosystems: Physics, Chemistry, Mathematics
Volume: 12
Number: 1
Year: 2021
Doi: DOI 10.17586/2220-8054-2021-12-1-5-14

Submitted to the proceedings of the conference "Mathematical Challenge of Quantum Transport in Nanosystems. Pierre Duclos Workshop" - Saint Petersburg, September 14-16, 2020


In this paper we deal with two dimensional cubic Dirac equations appearing as effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schrödinger equations and prove the existence of standing waves bifurcating from one band-edge of the linear spectrum.

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