The creation of stable 1D and 2D localized modes in lossy nonlinear media is a fundamental
problem in optics and plasmonics. This article gives a mini review of theoretical methods …

We demonstrate the generation of vortex solitons in a model of dissipative optical media with
the singular anti-cubic (AC) nonlinearity, by launching a vorticity-carrying Gaussian input …

We propose a simple dissipative system with purely cubic defocusing nonlinearity and
nonuniform linear gain that can support stable localized dissipative vortex solitons with high …

We consider settings providing the existence of stable two-dimensional (2D) dissipative
solitons with zero and nonzero vorticity in optical media with quadratic (χ (2)) nonlinearity. To …

We address the existence and stability of fundamental, single-charged vortex, and double-
charged vortex gap solitons in two-dimensional quasiperiodic photonic lattices imprinted in …

We study collisions of moving nonlinear-Schrödinger solitons with a P T-symmetric dipole
embedded into the one-dimensional self-focusing or defocusing medium. Accurate …

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe
the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity …

The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing
the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied …

We demonstrate an experimental approach for creating spatially localized states in a
semiconductor microcavity laser. In particular, we shape the spatial gain profile of a quasi …

We propose two models for the creation of stable dissipative solitons in optical media with
the χ (2)(quadratic) nonlinearity. To compensate spatially uniform loss in both the …