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.
Borrelli, W., Carlone, R., Tentarelli, L., Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit, <<SIAM JOURNAL ON MATHEMATICAL ANALYSIS>>, 2019; 51 (2): 1046-1081. [doi:10.1137/18M1211714] [http://hdl.handle.net/10807/171323]
Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit
Borrelli, William;
2019
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.
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