Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity

DOI10.1016/J.CHAOS.2020.109783zbMath1489.35301arXiv2003.14137OpenAlexW3022732730MaRDI QIDQ2120688

Boris A. Malomed, Dumitru Mihalache, Peng-Fei Li

Publication date: 1 April 2022

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.14137

zbMATH Keywords

nonlinear Schrödinger equationvortex solitoncompeting cubic-quintic nonlinearitiesLévy index

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08) Fractional partial differential equations (35R11)

Related Items (27)

Fractional quantum couplers ⋮ Optical solitons of model with integrable equation for wave packet envelope ⋮ Stabilization of fundamental solitons in the nonlinear fractional Schrödinger equation with \(\text{PT}\)-symmetric nonlinear lattices ⋮ Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation ⋮ Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension ⋮ Solitons in spin-orbit-coupled systems with fractional spatial derivatives ⋮ Quadratic fractional solitons ⋮ Spatiotemporal soliton interaction of saturable nonlinear Schrödinger equations in spatial dimensions higher than 1 ⋮ Bright solitons in fractional coupler with spatially periodical modulated nonlinearity ⋮ Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities ⋮ Nondegenerate solitons in the integrable fractional coupled Hirota equation ⋮ Solitons in a coupled system of fractional nonlinear Schrödinger equations ⋮ Two-dimensional fractional \(\mathcal{PPT}\)-symmetric cubic-quintic NLS equation: double-loop symmetry breaking bifurcations, ghost states and dynamics ⋮ Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation ⋮ Stable and oscillating solitons of \(\mathcal{PT}\)-symmetric couplers with gain and loss in fractional dimension ⋮ Analysis and more general solutions of Einstein field equation in \(f(R, T)\) gravity ⋮ Fundamental, dipole, and vortex solitons in fractional nonlinear Schrödinger equation with a parity-time-symmetric periodic potential ⋮ Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation ⋮ Gray solitons in parity-time-symmetric localized potentials with fractional-order diffraction ⋮ Fast soliton interactions in cubic-quintic nonlinear media with weak dissipation ⋮ Necklace beams carrying fractional angular momentum in fractional systems with a saturable nonlinearity ⋮ Multiplicity and concentration results for local and fractional NLS equations with critical growth ⋮ Cubic-quartic optical solitons and conservation laws with Kudryashov's law of refractive index by extended trial function ⋮ Filamentation and stabilization of vortex solitons in nonlinear metamaterial waveguides ⋮ Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation ⋮ Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation by means of \textit{Lévy-index management} ⋮ Parameters controlling of vortex solitons in nonlocal nonlinear medium with gradually characteristic length

Cites Work

• Existence, stability, and scattering of bright vortices in the cubic-quintic nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Singular solutions and optical collapse
• Symmetric and asymmetric solitons and vortices in linearly coupled two-dimensional waveguides with the cubic-quintic nonlinearity
• Spatial hysteresis and optical patterns
• Newton-conjugate-gradient methods for solitary wave computations
• Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity
• Fractional quantum mechanics and Lévy path integrals
• Schrödinger equations with fractional Laplacians
• Accessible solitons of fractional dimension
• Spectrally stable encapsulated vortices for nonlinear Schrödinger equations
• Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium
• Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
• Soliton dynamics in a fractional complex Ginzburg-Landau model
• Symmetry breaking of spatial Kerr solitons in fractional dimension
• Variational approach for breathers in a nonlinear fractional Schrödinger equation
• The fractional discrete nonlinear Schrödinger equation
• Fractional optical solitons
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Auto-waveguide propagation and the collapse of spiral light beams in non-linear media
• The Theory of Spiral Laser Beams in Nonlinear Media
• Unified approach to strings and vortices with soliton solutions
• On the nonlocality of the fractional Schrödinger equation
• Numerical study of fractional nonlinear Schrödinger equations
• Fractional Schrödinger equation for a particle moving in a potential well
• Stability of spinning ring solitons of the cubic-quintic nonlinear Schrödinger equation
• Stability of vortex solitons in the cubic-quintic model
• Fraction‐Dimensional Accessible Solitons in a Parity‐Time Symmetric Potential

This page was built for publication: Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity