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 …

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and
diverse branches of physics such as optics, plasmas, condensed matter physics, fluid …

We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-
Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order …

We introduce a class of spiraling anomalous vortex beam (AVB) arrays in strongly nonlocal
nonlinear media. The general analytical formula for the arrays is derived, and its …

Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-
2D Bose-Einstein condensates consisting of atoms with dipole moments polarized …

We show that metastable ring-shaped clusters can be constructed from two-dimensional
quantum droplets in systems described by the Gross-Pitaevskii equations augmented with …

The structure and stability of multipole and vortex solitons in the nonlocal nonlinear
fractional Schrödinger equation with a gradually decreasing Lévy index, α, are numerically …

We demonstrate that the fractional cubic-quintic nonlinear Schrödinger equation,
characterized by its Lévy index, maintains ring-shaped soliton clusters (“necklaces") carrying …

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the
interface between a dielectric medium (air) and a nonlinear material with a very long-range …

The existence and stability of fundamental, dipole, and tripole solitons in Kerr nonlinear
media with parity-time-symmetric Gaussian complex potentials are reported. Fundamental …