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 (Kirchho ) 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 L2-norm is indeed a saddle point.
On the structure of critical energy levels for the cubic focusing NLS on star graphs
Finco D;
2012-01-01
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 Schr odinger equation on the three-edge star graph with a free (Kirchho ) 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 L2-norm is indeed a saddle point.File in questo prodotto:
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