Multidimensional dissipative solitons and solitary vortices
arXiv:2208.01071 · doi:10.1016/j.chaos.2022.112526
Abstract
This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or dispersion, and between loss and gain. Due to these conditions, dissipative solitons (DSs) exist not in families, but as isolated solutions. The main issue is stability of 2D and 3D DSs, especially vortical ones. First, stable 2D DSs are presented in the framework of the complex Ginzburg-Landau equation with the cubic-quintic (CQ) nonlinearity, which combines linear and quintic loss with cubic gain. In addition to fundamental (zero-vorticity) DSs, stable spiral DSs are presented too, with vorticities 1 and 2. Stable 2D solitons were also found in a system of two linearly-coupled fields, with linear gain acting in one and linear loss in the other. In this case, the cubic loss (without quintic terms) is sufficient for the stability of fundamental and vortex DSs. In addition to truly localized states, weakly localized ones are presented too, in a model with nonlinear loss without explicit gain, the losses being compensated by influx of power from infinity. Other classes of 2D models which are considered here use spatially modulated loss or gain to predict many species of robust DSs, including ones featuring complex periodically recurring metamorphoses. Stable fundamental and vortex solitons are also produced by models with a trapping or spatially periodic potential. In the latter case, 2D gap DSs are considered. Further, 2D dissipative models with spin-orbit coupling give rise to stable semi-vortices, with vorticity carried by one component. Along with the 2D solitons, the review includes 3D fundamental and vortex DSs, stabilized by the CQ nonlinearity and/or external potentials, and collisions between them.
arXiv commenta review article to be published in Chaos, Solitons & Fractals (special issue on "New trends on instabilities and nonequilibrium structures"
References in corpus (48)
- Photonic Floquet Topological Insulators
- The World of the Complex Ginzburg-Landau Equation
- Nonlinear waves in -symmetric systems
- Spin-orbit coupling in quantum gases
- Observation of Half Quantum Vortices in an Exciton-Polariton Condensate
- Nonlinear switching and solitons in PT-symmetric photonic systems
- Edge Solitons in Nonlinear Photonic Topological Insulators
- Fundamental and vortex solitons in a two-dimensional optical lattice
- Stability analysis for solitons in PT-symmetric optical lattices
- Multidimensional solitons in periodic potentials
- Single vortex-antivortex pair in an exciton polariton condensate
- Engineering spin-orbit coupling for photons and polaritons in microstructures
- Vortex solitons: Old results and new perspectives
- Multidimensional solitons: Well-established results and novel findings
- Bright solitary matter waves: formation, stability and interactions
- Non-linear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses
- Absolutely stable solitons in two-component active systems
- Spin Textures of Polariton Condensates in a Tunable Microcavity with Strong Spin-Orbit Interaction
- Matter-wave gap vortices in optical lattices
- On-demand harnessing of photonic soliton molecules
- The variety of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses
- A Potential of Interaction between Two- and Three-Dimensional Solitons
- Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
- Effect of TE-TM Splitting on the topological stability of half-vortices in exciton-polariton condensates
- Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps
- Radially symmetric and azimuthally modulated vortex solitons supported by localized gain
- Symmetry breaking of solitons in two-dimensional complex potentials
- Discrete solitons and vortices on two-dimensional lattices of -symmetric couplers
- Spatiotemporal dissipative solitons and vortices in a multi-transverse-mode fiber laser
- Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics
- From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency selective feedback
- Observation of mode-locked spatial laser solitons
- Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials
- Spin-orbit coupling and crystal-field splitting in the electronic and optical properties of nitride quantum dots with a wurtzite crystal structure
- Controlling the optical spin Hall effect with light
- Localized solutions of Lugiato-Lefever equations with focused pump
- Two-dimensional dissipative gap solitons
- Pattern formation by kicked solitons in the two-dimensionnal Ginzburg-Landau medium with a transverse grating
- Azimuthons and pattern formation in annularly confined exciton-polariton Bose-Einstein condensates
- Non-diffracting and non-attenuating vortex light beams in media with nonlinear absorption of orbital angular momentum
- Stabilization of vortex beams in Kerr media by nonlinear absorption
- Clusters of cavity solitons bounded by conical radiation
- One- and two-dimensional modes in the complex Ginzburg-Landau equation with a trapping potential
- Vortex modes supported by spin-orbit coupling in a laser with saturable absorption
- Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain
- Spin-orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap
- A "metaphorical" nonlinear multimode fiber laser approach to weakly-dissipative Bose-Einstein condensates
- Rotating azimuthons in dissipative Kerr media excited by superpositions of Bessel beams