One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice

Abstract

The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The nonlinear potential landscape can balance the fractional-order diffraction and thus stabilizes the solitons, making the model unique and governed by the recently introduced fractional Schrödinger equation with a self-focusing cubic nonlinear lattice. Both 1D fundamental and multihump solitons (in forms of dipole and tripole ones) are found, which occupy one or three cells of the nonlinear lattice respectively, depending on the soliton's power (intensity). We find that the profiles of the predicted soliton families are impacted intensely by the Lévy index $\alpha$ which denotes the level of fractional Laplacian, so does to their stability. The stabilization of soliton families is possible if $\alpha$ exceeds a threshold value, below which the balance between fractional-order diffraction and the spatially modulated focusing nonlinearity will be broken.

4 pages, 6 figures

References in corpus (5)

• Fractional Quantum Mechanics
• Spatiotemporal accessible solitons in fractional dimensions
• A purely Kerr nonlinear model admitting flat-top solitons
• Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
• Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices

Cited by in corpus (18)

• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Symmetry breaking of spatial Kerr solitons in fractional dimension
• 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
• Localized modes and dark solitons sustained by nonlinear defects
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• 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
• Second-harmonic generation in the system with fractional diffraction
• Domain walls in fractional media
• Localized modes in nonlinear fractional systems with deep lattices
• One-dimensional L{é}vy Quasicrystal
• Self-trapped spatially localized states in combined linear-nonlinear periodic potentials
• Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity
• Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential