Wednesday, February 15, 2012

1202.2890 (Riccardo Adami et al.)

On the structure of critical energy levels for the cubic focusing NLS on
star graphs

Riccardo Adami, Claudio Cacciapuoti, Domenico Finco, Diego Noja
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
Schr\"odinger 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.
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