In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the bound states (arising as critical points of the NLD action functional) and we prove that, in the L^2 -subcritical case, they converge to the bound states of the nonlinear Schr"odinger equation in the nonrelativistic limit.
Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit / Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 51:2(2019), pp. 1046-1081.
Titolo: | Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit |
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Data di pubblicazione: | 2019 |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1137/18M1211714 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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Borrelli W., Carlone R. Tentarelli L. - Nonlinear Dirac equation on graphs with localized nonlinearities: bound states and nonrelativistic limit, 2019.pdf | 2a Post-print versione editoriale / Version of Record | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri | |
Borrelli_Carlone_Tentarelli_revised.pdf | 2. Post-print / Author's Accepted Manuscript | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2771914