On the nonlinear Dirac equation on noncompact metric graphs

William Borrelli, Raffaele Carlone, Lorenzo Tentarelli

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., |ψ|p−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.
Original languageEnglish
Pages (from-to)326-357
Number of pages32
JournalJournal of Differential Equations
Volume278
DOIs
Publication statusPublished - 2021

Keywords

  • Bound states
  • Local well-posedness
  • Metric graphs
  • Nonlinear Dirac equation
  • Nonrelativistic limit
  • Perturbation method

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