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 $L^2$-subcritical case, they converge to the bound states of the nonlinear Schrödinger equation in the nonrelativistic limit.

Keywords

  1. nonlinear Dirac equations
  2. metric graphs
  3. nonrelativistic limit
  4. variational methods
  5. bound states
  6. linking

MSC codes

  1. 35R02
  2. 35Q41
  3. 81Q35
  4. 49J35
  5. 58E05

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 1046 - 1081
ISSN (online): 1095-7154

History

Submitted: 4 September 2018
Accepted: 1 February 2019
Published online: 2 April 2019

Keywords

  1. nonlinear Dirac equations
  2. metric graphs
  3. nonrelativistic limit
  4. variational methods
  5. bound states
  6. linking

MSC codes

  1. 35R02
  2. 35Q41
  3. 81Q35
  4. 49J35
  5. 58E05

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