Nonlinear Schrödinger equation on graphs: recent results and open problems

D Noja - Philosophical Transactions of the Royal Society …, 2014 - royalsocietypublishing.org
In this paper, an introduction to the new subject of nonlinear dispersive Hamiltonian
equations on graphs is given. The focus is on recently established properties of solutions in …

[HTML][HTML] Variational properties and orbital stability of standing waves for NLS equation on a star graph

R Adami, C Cacciapuoti, D Finco, D Noja - Journal of Differential Equations, 2014 - Elsevier
We study standing waves for a nonlinear Schrödinger equation on a star graph G, ie N
halflines joined at a vertex. At the vertex an interaction occurs described by a boundary …