247 research outputs found
Bifurcating standing waves for effective equations in gapped honeycomb structures
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 Schr\"odinger equations and prove the existence of standing
waves bifurcating from one band-edge of the linear spectrum.Comment: Submitted to the proceedings of the conference "Mathematical
Challenge of Quantum Transport in Nanosystems. Pierre Duclos Workshop" -
Saint Petersburg, September 14-16, 202
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