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.
Lingua originale | English |
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pagine (da-a) | 326-357 |
Numero di pagine | 32 |
Rivista | Journal of Differential Equations |
Volume | 278 |
DOI | |
Stato di pubblicazione | Pubblicato - 2021 |
Keywords
- Bound states
- Local well-posedness
- Metric graphs
- Nonlinear Dirac equation
- Nonrelativistic limit
- Perturbation method