Stable and oscillating solitons of $$\pmb {\mathcal {PT}}$$-symmetric couplers with gain and loss in fractional dimension

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

“…In addition to the axisymmetric stationary vortex solitons, it is relevant to consider the dynamics of necklace-shaped clusters composed, at z = 0, as sets (circular chains) of M fundamental solitons (with zero intrinsic winding numbers) initially built with equal distances between them: l = 2R sin(π/M), (44) and global vorticity, S = 1, 2, 3, . .…”

“…The modulational instability of continuous waves [17] and many types of optical solitons produced by fractional NLSEs has been theoretically investigated, chiefly by means of numerical methods. These are quasi-linear "accessible solitons" (actually, quasi-linear modes) [20,21], gap solitons supported by spatially periodic (lattice) potentials [26][27][28][29][30], solitary vortices [31,32], multi-pole and multi-peak solitons [33][34][35][36], soliton clusters [37], and solitary states with spontaneously broken symmetry [40][41][42], as well as solitons in optical couplers [43,44]. Dissipative solitons in fractional complex Ginzburg-Landau equation (CGLE) were studied too [39].…”

Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices

“…Recently there are growing research activities on -symmetric non-Hermitian systems with complex potentials whose real (imaginary) part is an even (odd) function in various fields of science and engineering ( Konotop et al., 2016 ; Suchkov et al., 2016 ; Feng et al., 2017 ; El-Ganain et al., 2018 ; Miri and Alú, 2019 ). In particular, unconventional beam dynamics ( Makris et al., 2008 ) and nonlinear waves ( Musslimani et al., 2008 ; Kartashov et al., 2016 ) have been widely explored in -symmetric systems ( Konotop et al., 2016 ; Abdou et al., 2021 ; Zeng et al., 2021 ). The study of solitons in -symmetric optical and photonic lattices is, however, limited to low-dimensional cases ( Konotop et al., 2016 ; Suchkov et al., 2016 ; Zeng and Lan, 2012 ; Muniz et al., 2019 ; Zhu et al., 2013 ).…”

Quadratic fractional solitons

“…Further, realization of the propagation dynamics of light beams governed by this equation was proposed [50], and its extension for the model including the PT symmetry was put forward too [51]. Many types of optical solitons produced by fractional NLSEs have been theoretically investigated [52]- [79], such as "accessible solitons" [54,55], GSs [59][60][61][62][63], solitary vortices [64,65], multipole and multi-peak solitons [66][67][68][69], soliton clusters [70], symmetrybreaking solitons [73][74][75] as well as solitons in couplers [77][78][79].…”