Abstract:We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation… Show more
“…Besides the interactions between two soliton, we can also discuss the two-soliton bounded state, currently termed “soliton molecules” [11] , [12] . Fig.…”
Section: Results Discussionmentioning
confidence: 99%
“…A soliton is known as a self-reinforcing wave packet that keeps its shape and propagating velocity. Soliton exhibits its rich structures including optical soliton [1] , plane soliton [2] , soliton molecules [3] , rogue waves [4] , etc., and helps develop some breakthrough branches of physical sciences [5] , [6] , [7] such as optics, condense physics, fluid and plasma [8] , [9] , [10] , [11] .…”
“…Besides the interactions between two soliton, we can also discuss the two-soliton bounded state, currently termed “soliton molecules” [11] , [12] . Fig.…”
Section: Results Discussionmentioning
confidence: 99%
“…A soliton is known as a self-reinforcing wave packet that keeps its shape and propagating velocity. Soliton exhibits its rich structures including optical soliton [1] , plane soliton [2] , soliton molecules [3] , rogue waves [4] , etc., and helps develop some breakthrough branches of physical sciences [5] , [6] , [7] such as optics, condense physics, fluid and plasma [8] , [9] , [10] , [11] .…”
We address effects of spin-orbit coupling (SOC), phenomenologically added to a two-component Bose-Einstein condensate composed of particles moving by Lévy flights, in one-and two-dimensional (1D) and (2D) settings. The corresponding system of coupled Gross-Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Lévy index, α < 2 (the normal kinetic energy corresponds to α = 2). The SOC terms, with strength λ, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex (SV) and mixed-mode (MM) types in the interval of 1 < α < 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At λ → 0, amplitudes of these solitons vanish ∼ λ 1/(α−1) .
“…The dynamics of vortex solitons and vorticity-carrying ring-shaped soliton clusters were recently addressed in Reference [31,35,48] in the framework of the factional NLSE with the following cubic-quintic nonlinearity:…”
Section: Vortex Modes In Two-dimensional (2d) Fractional-diffraction ...mentioning
The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrödinger equation (NLSE) including fractional one-dimensional or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too, in particular, for fast moving solitons and the results produced by the variational approximation. Moreover, dissipative solitons are briefly considered, which are governed by the fractional complex Ginzburg–Landau equation.
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