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. https://basepub.dauphine.fr/handle/123456789/18564
TypeDocument de travail / Working paper
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
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 / Keywordsmetric graphs; NLS; NLD; ground states; bound states; localized nonlinearity; nonrelativistic limit
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