Bifurcating standing waves for effective equations in gapped honeycomb structures
Analysis of PDEs
2021-01-01 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.2012.14680,
title = {Bifurcating standing waves for effective equations in gapped honeycomb structures},
author = {William Borrelli and Raffaele Carlone},
journal= {arXiv preprint arXiv:2012.14680},
year = {2021}
}
Comments
Submitted to the proceedings of the conference "Mathematical Challenge of Quantum Transport in Nanosystems. Pierre Duclos Workshop" - Saint Petersburg, September 14-16, 2020