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Nanosystems: Physics, Chemistry, Mathematics, 2021, Volume 12, Issue 1, Pages 5–14
DOI: https://doi.org/10.17586/2220-8054-2021-12-1-5-14 (Mi nano582) 		 
MATHEMATICS

Bifurcating standing waves for effective equations in gapped honeycomb structures

W. Borrellia, R. Carloneb

a Centro De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri 3, I-56100, Pisa, Italy
b Universita “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, MSA, via Cinthia, I-80126, Napoli, Italy
Full-text PDF (238 kB)
DOI: https://doi.org/10.17586/2220-8054-2021-12-1-5-14
Abstract: 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 Schrödinger equations and prove the existence of standing waves bifurcating from one band-edge of the linear spectrum.
Keywords: nonlinear Dirac equations, bifurcation methods, existence results, honeycomb structures.
Received: 28.12.2020
Revised: 06.01.2021
Bibliographic databases:
Document Type: Article
PACS: 03.65.-w, 02.30.Rz
Language: English
Citation: W. Borrelli, R. Carlone, “Bifurcating standing waves for effective equations in gapped honeycomb structures”, Nanosystems: Physics, Chemistry, Mathematics, 12:1 (2021), 5–14
Citation in format AMSBIB
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\by W.~Borrelli, R.~Carlone
\paper Bifurcating standing waves for effective equations in gapped honeycomb structures
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2021
\vol 12
\issue 1
\pages 5--14
\mathnet{http://mi.mathnet.ru/nano582}
\crossref{https://doi.org/10.17586/2220-8054-2021-12-1-5-14}
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\elib{https://elibrary.ru/item.asp?id=45945476}
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