Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit
Analysis of PDEs
2019-04-11 v2 Mathematical Physics
math.MP
Quantum Physics
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 -subcritical case, they converge to the bound states of the NLS equation in the nonrelativistic limit.
Keywords
Cite
@article{arxiv.1807.06937,
title = {Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit},
author = {William Borrelli and Raffaele Carlone and Lorenzo Tentarelli},
journal= {arXiv preprint arXiv:1807.06937},
year = {2019}
}
Comments
34 pages, 4 figures. Keywords: nonlinear Dirac equations, metric graphs, nonrelativistic limit, variational methods, bound states, linking. Some minor revisions have been made with respect the previous version