Double-hump solitons in fractional dimensions with a 𝒫𝒯–symmetric potential

Abstract

We investigate the properties of double-hump solitons supported by the nonlinear Schrödinger equation featuring a combination of parity-time symmetry and fractional-order diffraction effect. Two classes of nonlinear states, i.e., out-of-phase and in-phase solitons are found. Each class contains two families of solitons originating from the same linear mode in both focusing and defocusing nonlinear Kerr media. The critical phase-transition point increases monotonously with increasing Lévy index. For strong gain and loss, out-of-phase solitons in focusing media are stable in a wide parameter window and are almost completely unstable in media with a defocusing nonlinearity. The stability of in-phase solitons is opposite to that of out-of-phase solitons. In-phase solitons in defocusing media are stable in their entire existence domains provided that the gain-loss strength is below a critical value. Meanwhile, the stability region shrinks with the decrease of Lévy index. We, thus, put forward the first example of spatial solitons in fractional dimensions with a parity-time symmetry.

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

“…Since then, interesting results on generating and manipulating linear and nonlinear propagation dynamics of laser beams in such fractional optical models were obtained. Some typical works include: Gaus- * zengjh@opt.ac.cn sian beams either evolved into diffraction-free beams [14] or undergone conical diffraction [15] during propagation without a potential, PT symmetry [16] and propagation dynamics of the super-Gaussian beams [17] , optical beams propagation with a harmonic potential [14,15,17] (which supports spatiotemporal accessible solitons too [18,19]) and periodic potentials [16,20], propagation management of light beams in a double-barrier potential [21], in the context of linear FSE regime; and in terms of nonlinear fractional Schrödinger equation (NLFSE) regime [22][23][24][25][26][27][28], including optical solitons (or solitary waves) without external potential [23,24], solitons supported by linear [25][26][27] and nonlinear [28] periodic potentials which refer, respectively, to optical lattice and nonlinear lattice as described below.…”

Solitons in the fractional Schrödinger equation with parity-time-symmetric lattice potential

“…Recently, PT symmetry in the spatial FSE was reported by Zhang et al, who showed that the nondiffracting propagation and conical diffraction of input beams were found at the critical point of a PT-symmetric lattice [26]. More recently, Dong et al have investigated double-hump solitons in the 1D NFSE with PT-symmetric potentials, and they found that the out-of-phase and in-phase solitons can be stable in focusing media and defocusing media, respectively [27]. Up to now, neither the combination of PT symmetry and lattice nor the higher-dimension solitons in the NFSE have been reported.…”

Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities

“…Since then, a number of striking properties have been reported in model of the FSE. [27][28][29][30] When the nonlinear effects have been considered in the FSE, a variety of fractional optical solitons can be produced by NLFSEs, [31] such as spatiotemporal accessible solitons, [32,33] double-hump solitons, [34] gap solitons, [35,36] nonlocal solitons, [37] www.advancedsciencenews.com www.ann-phys.org off-site and on-site vortex solitons, [38] bright solitons under the action of periodically spatially modulated nonlinearities, [39,40] dissipative surface solitons, [41] discrete solitons, [42] asymmetric solitons, [43] as well as vortex solitons in free space. [44] Optical solitons may undergo spontaneous symmetry breaking in conventional Hermitian and parity-time symmetric NLSE, an interesting generalization is to explore the symmetry breaking bifurcations of optical solitons in the NLFSE.…”