Inserted: 10 mar 2020
Last Updated: 10 mar 2020
Special Issue "Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks"
We present a brief overview of the existencenonexistence of standing waves for the NonLinear Schrödinger and the NonLinear Dirac Equations (NLSENLDE) on metric graphs with localized nonlinearity. First, we focus on the NLSE (both in the subcritical and the critical case) and, then, on the NLDE highlighting similarities and differences with the NLSE. Finally, we show how the two equations are related in the nonrelativistic limit by the convergence of the bound states.