TY - JOUR
T1 - On the nonlinear Dirac equation on noncompact metric graphs
AU - Borrelli, William
AU - Carlone, Raffaele
AU - Tentarelli, Lorenzo
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Bound states
KW - Local well-posedness
KW - Metric graphs
KW - Nonlinear Dirac equation
KW - Nonrelativistic limit
KW - Perturbation method
KW - Bound states
KW - Local well-posedness
KW - Metric graphs
KW - Nonlinear Dirac equation
KW - Nonrelativistic limit
KW - Perturbation method
UR - http://hdl.handle.net/10807/171311
U2 - 10.1016/j.jde.2021.01.005
DO - 10.1016/j.jde.2021.01.005
M3 - Article
SN - 0022-0396
VL - 278
SP - 326
EP - 357
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -