Calculus of Variations and Geometric Measure Theory

W. Borrelli - R. Carlone - L. Tentarelli

An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity

created by borrelli on 10 Mar 2020
modified by tentarelli on 07 Jul 2022


Published Paper

Inserted: 10 mar 2020
Last Updated: 7 jul 2022

Journal: Symmetry
Volume: 11
Number: 2
Pages: art. 169, 22pp
Year: 2019
Doi: 10.3390/sym11020169

ArXiv: 1901.02696 PDF

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.