A comparative review is given of some well-known and some recent results obtained in
studies of two-and three-dimensional (2D and 3D) solitons, with emphasis on states carrying …

During the past decade there has been an increased interest in the study of localized
structures in optics and in the area of matter waves [atomic Bose-Einstein condensates …

We analyze the existence and stability of two kinds of self-trapped spatially localized gap
modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional …

We predict solitary vortices in quasiplanar condensates of dipolar atoms, polarized parallel
to the confinement direction, with the effective sign of the dipole-dipole interaction inverted …

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates
(BEC's) loaded into optical lattices, are often described by the nonlinear Schrödinger or …

A possibility of creation of stable optical solitons combining one continuous and one discrete
coordinates, with embedded vorticity, in an array of planar waveguides with intrinsic cubic …

We introduce a two-dimensional model of a laser cavity based on the complex Ginzburg-
Landau equation with the cubic-quintic nonlinearity and a lattice potential accounting for the …

Complex Ginzburg-Landau (CGL) models of laser media (with cubic-quintic nonlinearity) do
not contain an effective diffusion term, which makes all vortex solitons unstable in these …

By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of
parallel linearly coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give …

We introduce a model of media with the cubic attractive nonlinearity concentrated along a
single or double stripe in the two-dimensional (2D) plane. The model can be realized in …