On the structure of critical energy levels for the cubic focusing NLS on star graphs
Riccardo AdamiDipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R Cozzi 53, 20125 Milan, ItalyClaudio CacciapuotiHausdorff Center for Mathematics, Institut f?r Angewandte Mathematik, 60 Endenicher Allee, 53115 Bonn, GermanyDomenico FincoFacoltà di Ingegneria, Università Telematica Internazionale Uninettuno, Corso Vittorio Emanuele II 39, 00186 Rome, ItalyDiego NojaDipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R Cozzi 53, 20125 Milan, Italy
2012en
ABI
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Abstract. We provide information on a non trivial structure of phase space of the cubic NLS on a three-edge star graph. We prove that, contrarily to the case of the standard NLS on the line, the energy associated to the cubic focusing Schrödinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant L2-norm. We moreover show that the only stationary state with prescribed L2-norm is indeed a saddle point. 1.
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