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arXiv · 1202.2890

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

Riccardo Adami·Claudio Cacciapuoti·Domenico Finco·Diego Noja
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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 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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Riccardo Adami, Claudio Cacciapuoti, Domenico Finco, Diego Noja. 2012-02-13. On the structure of critical energy levels for the cubic focusing NLS on star graphs. https://doi.org/10.1088/1751-8113/45/19/192001

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