We predict the existence of gap solitons in nonlinear fractional Schrödinger equation (NLFSE) with an imprinted optically harmonic lattice. Symmetric/antisymmetric localized modes bifurcate from lower/upper edge first/second band defocusing/focusing Kerr media. A unique feature we revealed is that, focusing media, stable appear finite bandgaps decrease Lévy index, which sharp contrast to standard NLSE a nonlinearity. Nonlinear bound states composed by in-phase and out-of-phase soliton units...

We predict a new type of two- and three-dimensional stable quantum droplets persistently rotating in broad external two-dimensional weakly anharmonic potential. Their evolution is described by the system Gross-Pitaevskii equations with Lee-Huang-Yang corrections. Such resemble whispering-gallery modes localized polar direction due to nonlinear interactions and, depending on their chemical potential rotation frequency, they appear rich variety shapes, ranging from nearly flat-top or strongly...

Generalization of Fractional Schrödinger equation (FSE) into optics is fundamentally important, since usually provides a fertile ground where FSE-related phenomena can be effectively observed. Beam propagation management topic considerable interest in the field optics. Here, we put forward simple scheme for realization light beams by introducing double-barrier potential FSE. Transmission, partial transmission/reflection, and total reflection fields controlled varying depth. Oblique input...

We investigate the properties of double-hump solitons supported by nonlinear Schrödinger equation featuring a combination parity-time symmetry and fractional-order diffraction effect. Two classes states, i.e., out-of-phase in-phase are found. Each class contains two families originating from same linear mode in both focusing defocusing Kerr media. The critical phase-transition point increases monotonously with increasing Lévy index. For strong gain loss, media stable wide parameter window...

We address the propagation dynamics of gap solitons at interface between uniform media and an optical lattice in framework a nonlinear fractional Schrödinger equation. Different families residing first second bandgaps Floquet-Bloch spectrum are revealed. They feature combination unique properties diffraction effects, surface waves solitons. The instability can be remarkably suppressed by decrease Lévy index, especially obvious for gaps. Additionally, we study multi-peaked dimensions find...

We address the formation of topological states in twisted circular waveguide arrays and find that twisting leads to important differences fundamental properties new vortex solitons with opposite charges arise nonlinear regime. such system features rare property clockwise counterclockwise are nonequivalent. Focusing on ${\mathcal{C}}_{6v}$ discrete rotation symmetry, we a longitudinal twist stabilizes lowest $m=\ifmmode\pm\else\textpm\fi{}1$, which always unstable untwisted same symmetry....

We put forward a model for trapping stable optical vortex solitons (VSs) with high topological charges m. The cubic-quintic nonlinear medium an imprinted ring-shaped modulation of the refractive index is shown to support two branches VSs, which are controlled by radius, width, and depth profile. While lower-branch VSs unstable in their nearly whole existence domain, upper branch completely stable. Vortex m ≤ 12 obey anti-Vakhitov-Kolokolov stability criterion. results suggest possibilities...

We present a theoretical scheme for generating vortex light bullets (LBs) in Rydberg atomic system. The stability property and propagation dynamics of LBs with different topological charges are investigated twisted circular waveguide arrays parity-time ($\mathcal{PT}$) symmetry. numerical solutions the corresponding nonlinear Schr\"odinger equation obtained by modified square operator method split-step Fourier method. longitudinal twist changes stabilities six-core enriches modulation...

We report the evolution of higher-order nonlinear states in a focusing cubic medium, where both linear refractive index and nonlinearity are spatially modulated by complex optical lattice exhibiting parity-time (PT) symmetry. reveal that introduction out-of-phase modulation makes possible stabilization solitons with number poles up to 7, which highly unstable PT lattices. Under appropriate conditions, multipole-mode components neighboring sites completely stable provided their power or...

We report the existence and stability properties of multipole-mode solitons supported by nonlinear Schrödinger equation featuring a combination fractional-order diffraction effect nonlocal focusing Kerr-type nonlinearity. reveal that solitons, including an arbitrary number peaks, can propagate stably in fractional systems provided propagation constant exceeds certain value, which is sharp contrast to conventional under normal diffraction, where bound states composed five peaks or more are...

We address the existence and stability of fundamental solitons in a -symmetric Gaussian potential embedded into material with fractional effects. Fundamental solitary waves low power both defocusing focusing medium originate from same eigenmode, smaller Levy index, narrower width solitons. The linear analysis has been carried out dimension. are completely stable for moderate index gain/loss coefficient wide region.

We address the existence and stability of multipole quantum droplets in symmetric binary Bose-Einstein condensates described by amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Quantum trapped a weakly anharmonic potential can be composed different numbers globally linked poles an azimuthally periodic distribution. Due to competing Lee-Huang-Yang-augmented nonlinearity, norm two branches slopes opposite sign merges together at lower cutoff chemical potential. The upper same...

We study the stability of multipole-mode solitons in one-dimensional thermal nonlinear media. show how sample geometry impacts mutlipole-mode and reveal that tripole quadrupole can be made stable their whole domain existence, provided width exceeds a critical value. In spite such geometry-dependent soliton stability, we find maximal number peaks media is same as materials with finite-range nonlocality.

We report the existence and stability properties of multipeaked solitons in a defocusing Kerr medium with an imprinted complex optical lattice featuring parity-time (PT) symmetry. Various families soliton solutions different number peaks are found first finite gap lattice. Linear analysis corroborated by direct propagation simulations reveals that can propagate stably wide range, provided their constant exceeds critical value. Our findings demonstrate, for time, stable PT-symmetric

We address the existence and stability properties of optical solitons in a competing cubic-quintic medium with an imprinted complex lattice featuring parity-time (𝒫𝒯) symmetry. Various families even odd geometrical symmetries are found both semi-infinite first finite gaps. Linear analysis corroborated by direct propagation simulations reveals that different number humps can propagate stably at same constants, i.e., multi-stable exist this scheme. Interestingly enough, sharp...

We study the existence and stability of dissipative surface solitons supported by nonlinear fractional Schrödinger equation (NLFSE) with an interface between a semi-infinite chirped lattice uniform Kerr medium. In such system, domain depends on upper cutoff value linear gain coefficient at fixed loss. The results analysis are in good agreement that propagation simulation dimension. Stable generally feature low energy small constants adapt to wide range two-photon absorption. instability can...

We put forward the existence of localized necklace solitons and ring in a defocusing cubic nonlinear medium with an imprinted Bessel optical lattice. Novel families are found their unique properties, including multistable states revealed. show that both could reside on any lattices. They dynamically stable provided lattice is modulated deep enough. The uncovered phenomena may open new way for soliton control manipulation.

We address the properties of wavepacket localization-delocalization transition (LDT) in fractional dimensions with a quasi-periodic lattice. The LDT point, which is generally determined by competition between two sub-lattices comprising lattice, turns out to be inversely proportional Lévy index. Surprisingly, we find that, presence weak structural disorder, anti-Anderson localization occurs, i.e., introduced disorder results an increasing size linear modes. Inclusion focusing nonlinearity...