Stability and nesting of dissipative vortex solitons with high vorticity

Aleksić, Branislav N.; Aleksić, Najdan B.; Škarka, V.; Belić, Milivoj R.

doi:10.1103/physreva.91.043832

Cited by 16 publications

(6 citation statements)

References 35 publications

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“…Lagrangian formally corresponding to Eq. ( 2) [47]. The same work reported the existence of stable concentric multiring states.…”

Section: Introductionmentioning

confidence: 80%

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Multidimensional dissipative solitons and solitary vortices

Malomed

2022

Preprint

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This article offers a review of (chiefly, theoretical) results for self-trapped states (solitons) in twoand three-dimensional (2D and 3D) models of nonlinear dissipative media. The existence of such solitons requires to maintain two stable balances: between nonlinear self-focusing and linear spreading (diffraction and/or dispersion) of the physical fields, and between losses and gain in the medium. Due to the interplay of these conditions, dissipative solitons exist, unlike solitons in conservative models, not in continuous families, but as isolated solutions (attractors). The main issue in the theory is stability of multidimensional dissipative solitons, especially ones with embedded vorticity. First, stable 2D dissipative solitons are presented in the framework of the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, which combines linear loss, cubic gain, and quintic loss (the linear loss is necessary to stabilize zero background around dissipative solitons, while the quintic loss provided for the global stability of the setting). In addition to fundamental (zero-vorticity) solitons, stable spiral solitons produced by the CGL equation are produced too, with intrinsic vorticities S = 1 and 2. Stable 2D solitons were also found in a system built of two linearly-coupled optical fields, with linear gain acting in one and linear loss, which plays the stabilizing role, in the other. In this case, the inclusion of the cubic loss (without quintic terms) is sufficient for the creation of stable fundamental and vortical dissipative solitons in the linearly-coupled system. In addition to truly localized states, weakly localized ones are presented too, in the single-component model with nonlinear losses, which does not include explicit gain. In that case, the losses are compensated by the influx of power from the reservoir provided, at the spatial infinity, by the weakly localized structure of the solution. Other classes of 2D models which are considered in this review make use of spatially modulated loss or gain to predict many species of robust dissipative solitons, including localized dynamical states featuring complex periodically recurring metamorphoses. Stable fundamental and vortical solitons are also produced by models including a trapping or spatially periodic potential. In the latter case, the consideration addresses 2D gap dissipative solitons as well. 2D two-component dissipative models including spin-orbit coupling are considered too. They give rise to stable states in the form of semi-vortex solitons, with vorticity carried by one component. In addition to the 2D solitons, the review includes 3D fundamental and vortical dissipative solitons, stabilized by the cubic-quintic nonlinearity and/or external potentials. Collisions between 3D dissipative solitons are considered too. Contents I. Introduction II. Spiral solitons (vortex rings) produced by the 2D complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity III. Dissipative vortex solitons in a laser cavity stabili...

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“…Lagrangian formally corresponding to Eq. ( 2) [47]. The same work reported the existence of stable concentric multiring states.…”

Section: Introductionmentioning

confidence: 80%

“…( 2): an inner VR with S = 3 embedded into the middle one one with S = 10, which is embedded into the outer VR with S = 20 (source: Ref. [47]). FIG.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional dissipative solitons and solitary vortices

Malomed

2022

Preprint

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“…For instance, Leblond et al proposed a reductive perturbation technique applied to 2D SGE to govern the propagation of femtosecond STSs in Kerr media [24]. For solving these equations, plenty of methods have been developed, such as Hirota bilinear method [25], Darboux transformation [26], variational method [27,28], and F-expansion method [29][30][31][32]. Among these techniques, F-expansion has attracted great interests due to its advantage of easy understanding and simple calculation.…”

Section: Introductionmentioning

confidence: 98%

Spatiotemporal soliton solution to generalized nonlinear Schrödinger equation with a parabolic potential in Kerr media

Kong

2016

Optics Communications

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“…In order to obtain solitons in the NLSE, it is necessary to find the balance between dispersion and nonlinearity, while in addition to that solitons in the CGLE must balance between (linear or nonlinear) gain and energy loss. Because of that soliton solutions of the CGLE do not form a continuous family like NLSE, but discrete solutions for given set of parameters (Uvarova and Burenok 2016;Aleksić et al 2012b;Skarka et al 2014;Aleksić et al 2015). Studies so far have revealed areas of stability for DS in CGLE with a nonzero conservative part of nonlinearity-the real part of nonlinear susceptibility (Kalashnikov et al 2006).…”

Section: Introductionmentioning

confidence: 99%

Dissipative structures in the resonant interaction of laser radiation with nonlinear dispersive medium

2021

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The article presents the results of studies on the stability of dissipative structures (DS) arising in the resonant interaction of laser radiation with a nonlinear medium. Resonant interaction is modeled by the one dimensional complex Ginzburg-Landau equation with a nonconservative cubic–quintic nonlinearity. The areas of existence of stable DS solutions have been determined analytically using a variational approach and confirmed numerically by extensive numerical simulations.

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Stability and nesting of dissipative vortex solitons with high vorticity

Cited by 16 publications

References 35 publications

Multidimensional dissipative solitons and solitary vortices

Multidimensional dissipative solitons and solitary vortices

Spatiotemporal soliton solution to generalized nonlinear Schrödinger equation with a parabolic potential in Kerr media

Dissipative structures in the resonant interaction of laser radiation with nonlinear dispersive medium

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