Dilute-gas Bose-Einstein condensates are an exceptionally versatile testbed for the investigation of novel solitonic structures. While matter-wave solitons in one-and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments, to the best of our knowledge. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright (DDB) solitons in a spinor F = 1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB states, as well as their robust oscillations in the trap.PACS numbers: 03.75. Mn, 03.75.Lm Solitons are localized waves propagating undistorted in nonlinear dispersive media. They play a key role in numerous physical contexts [1]. Among the various systems that support solitons, dilute-gas Bose-Einstein condensates (BECs) [2,3] provide a particularly versatile testbed for the investigation of solitonic structures [4][5][6]. In single-component BECs, solitons have been observed either as robust localized pulses (bright solitons) [7][8][9][10][11] or density dips in a background matter wave (dark solitons) [12][13][14][15][16][17][18][19][20][21], typically in BECs with attractive or repulsive interatomic interactions, respectively. Extending such studies to two-component BECs has led to rich additional dynamics. Solitons have been observed in binary mixtures of different spin states of the same atomic species, so-called pseudo-spinor BECs [22,23]. In particular, darkbright (DB) [24][25][26][27][28], and related SO(2) rotated states in the form of dark-dark solitons [29,30], have experimentally been created in binary 87 Rb BECs. Interestingly, although such BEC mixtures feature repulsive intra-and inter-component interactions, bright solitons do emerge due to an effective potential well created by the dark soliton through the intercomponent interaction [31]. Such mixed soliton states have been proposed for potential applications. Indeed, in the context of optics where these structures were pioneered [32,33], the dark soliton component was proposed to act as an adjustable waveguide for weak bright solitons [34]. In multicomponent BECs, compound solitons of the mixed type could also be used for all-matter-wave waveguiding, with the dark soliton building an effective conduit for the bright one, similar to all-optical waveguiding in optics [35]. Apart from pseudospinor BECs, such mixed soliton states have also been predicted to occur in genuinely spinorial BECs, composed of different Zeeman sub-levels of the same hyperfine state [36][37][38]. Indeed, pertinent works [39,40] have studied the existence and dynamic...

In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be unstable except in the vicinity of the linear limit. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well. The role of potential asymmetries in the nonlinearity or in the gain/loss pattern is also considered.

In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties also persists in the case of such wavepackets

In some interesting work of James Lidsey, the dynamics of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology with positive curvature and a perfect fluid matter source is shown to be modeled in terms of a time-dependent, harmonically trapped Bose-Einstein condensate. In the present work, we extend this dynamic correspondence to both FLRW and Bianchi I cosmologies in arbitrary dimension, especially when a cosmological constant is present.

We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the PT symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac) forcing is applied through periodic modulation of the coefficient accounting for the coupling of the two degrees of freedom. The system may be realized in optics as a dual-core waveguide with the gain and loss applied to different cores, and the thickness of the gap between them subject to a periodic modulation. The onset and development of the parametric instability for a small forcing amplitude (V1) is studied in an analytical form. The full dynamical chart of the system is generated by systematic simulations. At sufficiently large values of the forcing frequency, ω, tongues of the parametric instability originate, with the increase of V1, as predicted by the analysis. However, the tongues following further increase of V1 feature a pattern drastically different from that in usual (non-PT ) parametrically driven systems: instead of bending down to larger values of the dc coupling constant, V0, they maintain a direction parallel to the V1 axis. The system of the parallel tongues gets dense with the decrease of ω, merging into a complex small-scale structure of alternating regions of stability and instability. The cases of ω → 0 and ω → ∞ are studied analytically by means of the adiabatic and averaging approximation, respectively. The cubic nonlinearity, if added to the system, alters the picture, destabilizing many originally robust dynamical regimes, and stabilizing some which were unstable. Recently, a great deal of interest has been drawn to systems featuring the PT (parity-time) symmetry. Originally, they were introduced as quantum systems with spatially separated and symmetrically placed linear gain and loss. A fundamental property of non-Hermitian PT -symmetric Hamiltonians is the fact that their spectra remain purely real, like in the case of the usual Hermitian Hamiltonians, provided that the strength of the non-Hermitian part of the Hamiltonian, γ, does not exceed a certain critical value, γ cr , at which the PT symmetry breaks down. Such linear systems were recently implemented experimentally in optics, due to the fact that the paraxial propagation equation for electromagnetic waves can emulate the quantum-mechanical Schrödinger equation. In particular, the PT -symmetric quantum system may be emulated by waveguides with spatially separated mutually balanced gain and loss elements. Additional interest to the optical realizations of the PT symmetry has been drawn by the possibility to implement this setting in nonlinear waveguides. Unlike the ordinary models of nonlinear dissipative systems, where stable modes exist as isolated attractors, in PT -symmetric systems they emerge in continuous families, similar to what is commonly known about conservative nonlinear systems. However, the increase of the gain-loss coefficient, γ, leads to the shrinkage of existence and stability region...