Abstract Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …

We consider the dynamical model of quantum droplets (QDs) launched in a deep optical
lattice. This setting is modeled by a one-dimensional discrete Gross-Pitaevskii equation with …

What we believe is a new scheme for producing semidiscrete self-trapped vortices (“swirling
photon droplets”) in photonic crystals with competing quadratic (χ^(2)) and self-defocusing …

Solitons are nonlinear self-sustained wave excitations and probably among the most
interesting and exciting emergent nonlinear phenomenon in the corresponding theoretical …

We investigate the dynamics of dissipative quantum droplets (QDs) forming in one-
dimensional binary Bose gases subjected to three-body recombination loss and linear gain …

We numerically investigate the existence and stability of self-bound states forming in a one-
dimensional binary bosonic condensate confined in non-parity-time (PT)-symmetric complex …

This article presents a concise survey of basic discrete and semi-discrete nonlinear models,
which produce two-and three-dimensional (2D and 3D) solitons, and a summary of the main …

The formation and dynamics of full vortex gap solitons (FVGSs) are investigated in two-
component Bose–Einstein condensates with spin–orbit coupling (SOC), Zeeman splitting …

We demonstrate that both fundamental and multipole soliton families can be generated and
stabilized in purely saturable nonlinear lattices, which can be readily realized in nonlinear …

This concise review summarizes recent advancements in theoretical studies of vortex
quantum droplets (VQDs) in matter-wave fields. These are robust self-trapped vortical states …