Quadratic fractional solitons

Zeng, Liangwei; Zhu, Yongle; Malomed, Boris A.; Mihalache, Dumitru; Wang, Qing; Long, Hu; Cai, Yi; Lu, Xiaowei; Li, Jingzhen

doi:10.1016/j.chaos.2021.111586

Cited by 36 publications

(16 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, breaking and restoration of the solitons' P T symmetry were recently considered in Reference [16]. An interesting possibility is to introduce fractional equations of the NLSE type with quadratic or quadratic-cubic nonlinearity [47,69]. Furthermore, various modes supported by a modulationally stable background field (continuous wave) were theoretically considered, such as dark solitons and vortices, "bubbles", and W-shaped solitons [51,70].…”

Section: Discussionmentioning

confidence: 99%

“…eff /∂(W, N ) = 0, result in an expression showing how potential (47) with small Ω 2 lifts the norm degeneracy of the 2D Townes solitons.…”

Section: Stabilization Of 2d Solitons By the Trapping Potentialmentioning

confidence: 99%

“…In the case of quadratic self-focusing nonlinearity, the critical collapse occurs at α = 1/2; hence, the Lévy index may take values 1/2 < α ≤ 2 in that case. The quadratic self-focusing term appears on the right-hand side of Equation (1) in the form of −ε|ψ|ψ with ε > 0, as the correction induced by quantum fluctuations [46] to the 1D fractional Gross-Pitaevskii equation for the gas of Lévy-hopping particles [47].…”

Section: Introduction and The Basic Modelsmentioning

confidence: 99%

“…The stability and evolution of the solitons labeled by B1-B4 are displayed in Figure4. The plots are borrowed from Reference[47] (unpublished).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

Malomed

2021

Photonics

Self Cite

116

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

“…eff /∂(W, N ) = 0, result in an expression showing how potential (47) with small Ω 2 lifts the norm degeneracy of the 2D Townes solitons.…”

Section: Stabilization Of 2d Solitons By the Trapping Potentialmentioning

confidence: 99%

Section: Introduction and The Basic Modelsmentioning

confidence: 99%

“…The stability and evolution of the solitons labeled by B1-B4 are displayed in Figure4. The plots are borrowed from Reference[47] (unpublished).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

Malomed

2021

Photonics

Self Cite

116

View full text Add to dashboard Cite

show abstract

“…The emulation of the fractional diffraction in optics suggests to take into regard the natural Kerr nonlinearity of optical media, and thus to address a possibility of the existence of fractional solitons. Various aspects of this topic were a subject of many recent theoretical works [13]- [28], see also a review in Ref. [29].…”

Section: Introductionmentioning

confidence: 99%

One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy

Sakaguchi,

Malomed

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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) .

show abstract

Fractional Wave Models and Their Experimental Applications

Malomed

2024

Nonlinear Systems and Complexity

View full text Add to dashboard Cite

Quadratic fractional solitons

Cited by 36 publications

References 93 publications

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy

Fractional Wave Models and Their Experimental Applications

Contact Info

Product

Resources

About