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 Schrodinger equation in the nonrelativistic limit.
Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit / Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 51:2(2019), pp. 1046-1081. [10.1137/18M1211714]
Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit
BORRELLI, WILLIAM;Carlone, Raffaele;Tentarelli, Lorenzo
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 L-2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.| File | Dimensione | Formato | |
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