Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit

William Borrelli, Raffaele Carlone, Lorenzo Tentarelli

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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 L2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.
Original languageEnglish
Pages (from-to)1046-1081
Number of pages36
JournalSIAM Journal on Mathematical Analysis
Volume51
DOIs
Publication statusPublished - 2019

Keywords

  • Bound states
  • Linking
  • Metric graphs
  • Nonlinear Dirac equations
  • Nonrelativistic limit
  • Variational methods

Fingerprint

Dive into the research topics of 'Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit'. Together they form a unique fingerprint.

Cite this