najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-1-5-14najo-348Research ArticleMATHEMATICSМАТЕМАТИКАBifurcating standing waves for effective equations in gapped honeycomb structuresРасщепляющиеся стоячие волны для эффективных уравнений в гексагональных структурах с зазорамиBorrelliW.BorrelliW.

Piazza dei Cavalieri 3, I-56100, Pisa

Piazza dei Cavalieri 3, I-56100, Pisa

william.borrelli@sns.itCarloneR.CarloneR.

MSA, via Cinthia, I-80126, Napoli

MSA, via Cinthia, I-80126, Napoli

raffaele.carlone@unina.itCentro De Giorgi, Scuola Normale SuperioreCentro De Giorgi, Scuola Normale SuperioreUniversita “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Universita “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”202128072025121514Copyright © Borrelli W., Carlone R., 20252025Borrelli W., Carlone R.Borrelli W., Carlone R.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/348

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

В этой статье мы имеем дело с двумерными кубическими уравнениями Дирака, выступающими в качестве эффективной модели в гексагональных структурах с зазорами. Мы даем формальный вывод, исходя из кубических уравнений Шредингера, и доказываем существование стоячих волн, ответвляющихся от одного края полосы линейного спектра.

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The authors declare that there are no conflicts of interest present.