Riccardo Adami, Claudio Cacciapuoti, Domenico Finco, Diego Noja
On the structure of critical energy levels for the cubic focusing NLS on star graphs
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ABSTRACT. We provide information on a non trivial structure of the 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 Schroedinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant $L^2$-norm. We moreover show that the only stationary state with prescribed L^2-norm is indeed a saddle point.