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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

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Symmetry
Volume
11
Number
2
Published in
Paris
Pages
20
Publication identifier
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Author(s)
Borrelli, William
CEntre 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 limit