Constrained energy minimization and orbital stability for the NLS equation on a star graph (Rapporti tecnici/preprint/working paper)

Type

• Rapporti tecnici/preprint/working paper (Classe)
• Prodotto della ricerca (Classe)

Label

• Constrained energy minimization and orbital stability for the NLS equation on a star graph (Rapporti tecnici/preprint/working paper) (literal)

Anno

• 2012-01-01T00:00:00+01:00 (literal)

Alternative label

• Adami R.; Cacciapuoti C.; Finco D.; Noja D. (2012)
  Constrained energy minimization and orbital stability for the NLS equation on a star graph
  
  (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori

• Adami R.; Cacciapuoti C.; Finco D.; Noja D. (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url

• http://arxiv.org/abs/1211.1515 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#volumeInCollana

• 1211.1515v1 (literal)

Note

• Google Scholar (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni

• Dipartimento di Scienze Matematiche, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy; Hausdorff Center for Mathematics, Institut f?ur Angewandte Mathematik, Endenicher Allee, 60, 53115 Bonn, Germany; Facolt?a di Ingegneria, Universit?a Telematica Internazionale Uninettuno, Corso Vittorio Emanuele II 39, 00186 Roma, Italy; Dipartimento di Matematica e Applicazioni, Universit?a di Milano Bicocca, via R. Cozzi, 53, 20125 Milano, Italy (literal)

Titolo

• Constrained energy minimization and orbital stability for the NLS equation on a star graph (literal)

Abstract

• We consider a nonlinear Schr\"odinger equation with focusing nonlinearity of power type on a star graph ${\mathcal G}$, written as $ i \partial_t \Psi (t) = H \Psi (t) - |\Psi (t)|^{2\mu}\Psi (t)$, where $H$ is the selfadjoint operator which defines the linear dynamics on the graph with an attractive $\delta$ interaction, with strength $\alpha < 0$, at the vertex. The mass and energy functionals are conserved by the flow. We show that for {2}<\mu<2$ the energy at fixed mass is bounded from below and that for every mass $m$ below a critical mass $m^*$ it attains its minimum value at a certain $\hat \Psi_m \in H^1(\GG) $, while for $m>m^*$ there is no minimum. Moreover, the set of minimizers has the structure ${\mathcal M}={e^{i\theta}\hat \Psi_m, \theta\in \erre}$. Correspondingly, for every $m

Prodotto di

• Institute for applied mathematics and information technologies (IMATI) (Istituto)
• Sviluppo di competenze di modellistica per la realizzazione di grandi progetti industriali (SP.P01.003.001) (Modulo)

Autore CNR

• RICCARDO ADAMI (Persona)

Incoming links:

Prodotto

• Institute for applied mathematics and information technologies (IMATI) (Istituto)
• Sviluppo di competenze di modellistica per la realizzazione di grandi progetti industriali (SP.P01.003.001) (Modulo)

Autore CNR di

• RICCARDO ADAMI (Persona)