We reveal that spatially localized vortex solitons become stable in self-focusing nonlinear
media when the vortex symmetry-breaking azimuthal instability is eliminated by a nonlocal …

We study stability and dynamics of the single cylindrically symmetric solitary structures and
dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons …

We study static solutions of a D-dimensional modified nonlinear Schrödinger equation
(MNLSE) which was shown to describe, in two dimensions, the self-trapped (spontaneously …

Using asymptotic methods, we investigate whether discrete breathers are supported by a
two-dimensional Fermi–Pasta–Ulam lattice. A scalar (one-component) two-dimensional …

We investigate analytically and numerically the stability of multiply-charged two-dimensional
bright vortex solitons in media with focusing cubic and defocusing quintic nonlinearities. A …

We observe stable propagation of spatially localized single-and double-charge optical
vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of …

We consider a two-dimensional Fermi–Pasta–Ulam (FPU) lattice with hexagonal symmetry.
Using asymptotic methods based on small amplitude ansatz, at third order we obtain a …

We study the cubic-(focusing-) quintic (defocusing) nonlinear Schrödinger equation in two
transverse dimensions. We discuss a family of stationary traveling waves, including …

The modulational instability associated with discrete breathers in 2D quantum ultracold
atoms is studied by using the Glauber's coherent state combined with a semi-discrete …

We introduce a class of robust soliton clusters composed of N fundamental solitons in three-
dimensional media combining the self-focusing cubic and self-defocusing quintic …