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 …

We study a semiclassical asymptotics of the Cauchy problem for a time-dependent
Schrödinger equation on metric and decorated graphs with a localized initial function. A …

We investigate the existence of ground states for the subcritical NLS energy on metric
graphs. In particular, we find out a topological assumption that guarantees the nonexistence …

We investigate the existence of ground states with prescribed mass for the focusing
nonlinear Schrödinger equation with L 2-critical power nonlinearity on noncompact quantum …

We investigate the existence of ground states of prescribed mass, for the nonlinear
Schrödinger energy on a noncompact metric graph G. While in some cases the topology of …

We review evolutionary models on quantum graphs expressed by linear and nonlinear
partial differential equations. Existence and stability of the standing waves trapped on …

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 …

On a star graph made of N≥ 3 halflines (edges) we consider a Schrödinger equation with a
subcritical power-type nonlinearity and an attractive delta interaction located at the vertex …

On a star graph G, we consider a nonlinear Schrödinger equation with focusing nonlinearity
of power type and an attractive Dirac's delta potential located at the vertex. The equation can …

We consider a nonlinear Schrödinger equation (NLS) posed on a graph (or network)
composed of a generic compact part to which a finite number of half-lines are attached. We …