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

We provide an overview of recent experimental and theoretical developments in the area of
optical discrete solitons. By nature, discrete solitons represent self-trapped wavepackets in …

We present a progress overview focused on the recent theoretical and experimental
advances in the area of soliton manipulation in optical lattices. Optical lattices offer the …

We study the existence of ground state solutions for a class of discrete nonlinear
Schrödinger equations with a sign-changing potential V that converges at infinity and a …

We investigate, experimentally and theoretically, light propagation in one-dimensional
waveguide arrays exhibiting a saturable self-defocusing nonlinearity. We demonstrate low …

The observation of nonlinear staggered surface states at the interface between a substrate
and a one-dimensional self-defocusing nonlinear waveguide array is reported. Launching of …

We deal with the existence and multiplicity of homoclinic solutions for a class of periodic
discrete Schrödinger equations with local superquadratic conditions. The arising problem …

The long-standing problem of moving discrete solitary waves in nonlinear Schrödinger
lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity …

We analyze the existence and stability of localized solutions in the one-dimensional discrete
nonlinear Schrödinger (DNLS) equation with a combination of competing self-focusing cubic …

We address the issue of mobility of localized modes in two-dimensional nonlinear
Schrödinger lattices with saturable nonlinearity. This describes, eg, discrete spatial solitons …