We consider the nonlinear Schrödinger equation with pure power nonlinearity on a general compact metric graph, and in particular its stationary solutions with fixed mass. Since the the graph is compact, for every value of the mass there is a constant solution. Our scope is to analyze (in dependence of the mass) the variational properties of this solution, as a critical point of the energy functional: local and global minimality, and (orbital) stability. We consider both the subcritical regime and the critical one, in which the features of the graph become relevant. We describe how the above properties change according to the topology and the metric properties of the graph.

Variational and Stability Properties of Constant Solutions to the NLS Equation on Compact Metric Graphs

Cacciapuoti, Claudio;
2018-01-01

Abstract

We consider the nonlinear Schrödinger equation with pure power nonlinearity on a general compact metric graph, and in particular its stationary solutions with fixed mass. Since the the graph is compact, for every value of the mass there is a constant solution. Our scope is to analyze (in dependence of the mass) the variational properties of this solution, as a critical point of the energy functional: local and global minimality, and (orbital) stability. We consider both the subcritical regime and the critical one, in which the features of the graph become relevant. We describe how the above properties change according to the topology and the metric properties of the graph.
2018
http://springerlink.metapress.com/app/home/journal.asp?wasp=4h8ayhrhykcxt3wn9h2m&referrer=parent&backto=browsepublicationsresults,366,541;
critical growth; metric graphs; Nonlinear Schrödinger equation; stability; stationary solutions; Mathematics (all)
Cacciapuoti, Claudio; Dovetta, Simone; Serra, Enrico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2075023
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