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 …

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

We address the formation of topological states in twisted circular waveguide arrays and find
that twisting leads to important differences of the fundamental properties of new vortex …

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 …

The existence of thresholdless vortex solitons trapped at the core of disclination lattices that
realize higher-order topological insulators is reported. The study demonstrates the interplay …

We report the composite vortex solitons of three-wave mixing propagate stably in a three-
dimensional (3D) quasi-phase-matched photonic crystals (QPM-PhC). The modulation of …

We show that optical moiré lattices enable the existence of vortex solitons of different types
in self-focusing Kerr media. We address the properties of such states both in lattices having …

Periodic structures structured as photonic crystals and optical lattices are fascinating for
nonlinear waves engineering in the optics and ultracold atoms communities. Moiré photonic …

We introduce partially-parity-time (p PT)-symmetric azimuthal potentials composed from
individual PT-symmetric cells located on a ring, where two azimuthal directions are …

We consider vortex solitons in large-scale arrays composed of N elliptical waveguides
placed on a ring, which can be fabricated using fs-laser writing technique in transparent …