We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with 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.

On the structure of critical energy levels for the cubic focusing NLS on star graphs / Adami, Riccardo; Claudio, Cacciapuoti; Domenico, Finco; Diego, Noja. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 45:(2012), p. 192001. [10.1088/1751-8113/45/19/192001]

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

ADAMI, RICCARDO;
2012

Abstract

We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2573169
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