The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., |ψ|p−2ψ) on noncompact metric graphs with a finite number of edges, in the case of Kirchhoff-type vertex conditions. Precisely, we prove local well-posedness for the associated Cauchy problem in the operator domain and, for infinite N-star graphs, the existence of standing waves bifurcating from the trivial solution at ω=mc2, for any p>2. In the Appendix we also discuss the nonrelativistic limit of the Dirac-Kirchhoff operator.

On the nonlinear Dirac equation on noncompact metric graphs / Borrelli, W.; Carlone, R.; Tentarelli, L.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 278:(2021), pp. 326-357. [10.1016/j.jde.2021.01.005]

On the nonlinear Dirac equation on noncompact metric graphs

Tentarelli L.
2021

Abstract

The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., |ψ|p−2ψ) on noncompact metric graphs with a finite number of edges, in the case of Kirchhoff-type vertex conditions. Precisely, we prove local well-posedness for the associated Cauchy problem in the operator domain and, for infinite N-star graphs, the existence of standing waves bifurcating from the trivial solution at ω=mc2, for any p>2. In the Appendix we also discuss the nonrelativistic limit of the Dirac-Kirchhoff operator.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2869660