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 define the Schrödinger equation with focusing, cubic nonlinearity on one-vertex graphs.
We prove global well-posedness in the energy domain and conservation laws for some self …

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 …

We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear
Schrödinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line …

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 …

The propagation of probe beam through complex conductive medium is controlled and
modified by Laguerre fields. The maximum positive group index of 5.1× 10 5 and group …