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On the nonlinear Dirac equation on noncompact metric graphs

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1912.11459.pdf (331.7Kb)
Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
12-2019
Link to item file
https://hal.archives-ouvertes.fr/hal-02426035
Dewey
Analyse
Sujet
nonlinear Dirac equation; metric graphs; local well-posedness; bound states; implicit function theorem; bifurcation; perturbation method; nonrelativistic limit
URI
https://basepub.dauphine.fr/handle/123456789/20705
Collections
  • CEREMADE : Publications
Metadata
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Author
Borrelli, William
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carlone, Raffaele
42093 Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Tentarelli, Lorenzo
92732 Dipartimento di Matematica "Guido Castelnuovo" [Roma I] [Sapienza University of Rome]
Type
Document de travail / Working paper
Item number of pages
29
Abstract (EN)
The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., ψp−2ψ) on noncompact metric graphs with a finite number of edges, in the case of Kirchhoff-type vertex conditions. Precisely, we prove local well-posedness for the associated Cauchy problem in the operator domain and, for infinite N-star graphs, the existence of standing waves bifurcating from the trivial solution at ω=mc2, for any p>2. In the Appendix we also discuss the nonrelativistic limit of the Dirac-Kirchhoff operator.

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