One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Abstract

Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic-quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years---the nonlinear fractional Schrödinger equation (NLFSE), therefore obtaining the cubic-quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov-Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic-quintic nonlinear terms.

9 pages, 9 figures, accepted for publication

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Cited by in corpus (13)

• Propagation dynamics of the circular Airy Gaussian vortex beams in the fractional nonlinear Schrödinger equation
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities
• Quadratic fractional solitons
• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers
• Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media
• One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy
• Domain walls in fractional media
• Localized modes in nonlinear fractional systems with deep lattices
• One-dimensional L{é}vy Quasicrystal
• Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity