Nonlinear classical Hamiltonian lattices exhibit generic solutions—discrete breathers. They
are time-periodic and (typically exponentially) localized in space. The lattices have discrete …

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 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 study analytically and numerically the stability of the standing waves for a nonlinear
Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is …

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is
incident upon an evolving, broad potential barrier that arises from an appropriate variation of …

Solitons—self-localized robust and long-lived nonlinear solitary waves that do not disperse
and preserve their identity during propagation and after a collision—arise in any physical …

We present a unified approach for qualitative and quantitative analysis of stability and
instability dynamics of positive bright solitons in multidimensional focusing nonlinear media …

We consider a generalized nonlinear Schrödinger equation (NLS) with a power nonlinearity|
ψ| 2μ ψ of focusing type describing propagation on the ramified structure given by N edges …

We investigate the ground states of the one-dimensional nonlinear Schr\" odinger equation
with a defect located at a fixed point. The nonlinearity is focusing and consists of a subcritical …

We show that the scaling symmetry breaking in soliton scattering reveals the hidden role of
the soliton self-interaction (“binding”) energy and its dramatic impact on the wave-particle …