
An overview on the standing waves of nonlinear Schroedinger and Dirac equations on metric graphs with localized nonlinearity
Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo (2019), An overview on the standing waves of nonlinear Schroedinger and Dirac equations on metric graphs with localized nonlinearity, Symmetry, 11, 2, p. 20. 10.3390/sym11020169
Type
Article accepté pour publication ou publiéDate
2019Journal name
SymmetryVolume
11Number
2Published in
Paris
Pages
20
Publication identifier
Metadata
Show full item recordAuthor(s)
Borrelli, WilliamCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carlone, Raffaele
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Tentarelli, Lorenzo
Dipartimento di Matematica "Guido Castelnuovo" [Roma I] [Sapienza University of Rome]
Abstract (EN)
We present a brief overview on the existence/nonexistence of standing waves for the NonLinear Schrödinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs with localized nonlinearity. We first 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, proving the convergence of bound states.Subjects / Keywords
metric graphs; NLS; NLD; ground states; bound states; localized nonlinearity; nonrelativistic limitRelated items
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Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo (2019) Article accepté pour publication ou publié
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Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo (2019) Document de travail / Working paper
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