This article offers a comprehensive survey of results obtained for solitons and complex
nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially …

This article offers a review of (chiefly, theoretical) results for self-trapped states (solitons) in
two-and three-dimensional (2D and 3D) models of nonlinear dissipative media. The …

The existence and stability of quantum droplets are studied in ultracold atoms in Bose–
Einstein condensates with a radial period lattice under the Lee–Huang–Yang correction …

We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are
described by a two-dimensional (2D) Gross–Pitaevskii (GP) equation with a periodic …

We prove that the dark solitons can be stable in the purely quintic nonlinear lattices,
including the fundamental, tripole and five-pole solitons. These dark soliton families are …

We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped
quantum droplets (QDs) formed by binary Bose–Einstein condensates. The system is …

We find that the recently introduced model of self-trapping supported by a spatially growing
strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, ie, three …

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 …

We study the existence, stability, and mobility of fundamental discrete solitons in two-and
three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing …

We predict a variety of composite quiescent and spinning two-and three-dimensional (2D
and 3D) self-trapped modes in media with a repulsive nonlinearity whose local strength …