This review paper presents an overview of the theoretical and experimental progress on study matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing general framework, we discuss statics dynamics single multiple quasi one-dimensional setting, higher-dimensional settings, as well dimensionality crossover regime. Special attention is paid to connection between results, obtained by various analytical approaches, relevant observations.

The aim of the present review is to introduce reader some physical notions and mathematical methods that are relevant study nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing general framework, we discuss prototypical models this setting for different dimensions potentials confining atoms. We analyze model properties explore their typical wave solutions (plane solutions, bright, dark, gap solitons, as well vortices). then offer a collection can be used understand...

We report on the generation, subsequent oscillation and interaction of a pair matter-wave dark solitons. These are created by releasing Bose-Einstein condensate from double well potential into harmonic trap in crossover regime between one dimension three dimensions. Multiple oscillations collisions solitons observed, quantitative agreement with simulations Gross-Pitaevskii equation. An effective particle picture is developed confirms that deviation observed frequencies asymptotic prediction...

We study matter-wave bright solitons in spin-orbit coupled Bose-Einstein condensates with attractive interactions. use a multiscale expansion method to identify solution families for chemical potentials the semi-infinite gap of linear energy spectrum. Depending on and coupling strengths, may present either sech2-shaped or modulated density profile reminiscent stripe phase repulsive condensates. Our numerical results are excellent agreement our analytical findings demonstrate potential...

An experimentally realizable scheme of periodic sign-changing modulation the scattering length is proposed for Bose-Einstein condensates similar to dispersion-management schemes in fiber optics. Because controlling via Feshbach resonance, named Feshbach-resonance management. The modulational-instability analysis quasiuniform condensate driven by this leads an analog Kronig-Penney model. ensuing stable localized structures are found. These include breathers, which oscillate between...

We introduce the concept of ring dark solitons in Bose-Einstein condensates. show that relatively shallow rings are not subject to snake instability, but a deeper splits into robust ringlike cluster vortex pairs, which performs oscillations radial and azimuthal directions, following dynamics original soliton.

We revisit a classic study [D. S. Hall, Phys. Rev. Lett. 81, 1539 (1998)10.1103/PhysRevLett.81.1539] of interpenetrating Bose-Einstein condensates in the hyperfine states |F=1,m{f}=-1 identical with |1 and |F=2,m{f}=+1 |2 87Rb observe striking new nonequilibrium component separation dynamics form oscillating ringlike structures. The process is not significantly damped, finding that also contrasts sharply earlier experimental work, allowing clean first look at collective excitation binary...

In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities Bose-Einstein condensates in one- and two-dimensional settings. particular, illustrate trapping conditions that allow reduction three-dimensional, mean field description (through Gross-Pitaevskii equation) to such lower dimensional settings, as well lattice We then go study modulational instability one dimension snaking/transverse two dimensions typical examples long-wavelength...

We consider nonlinear analogues of Parity-Time (PT) symmetric linear systems exhibiting defocusing nonlinearities. study the ground state and excited states (dark solitons vortices) system report following remarkable features. For relatively weak values parameter $\varepsilon$ controlling strength PT-symmetric potential, undergo (analytically tractable) spontaneous symmetry breaking; as is further increased, first state, well branches higher multi-soliton (multi-vortex) states, collide in...

In this review we try to capture some of the recent excitement induced by experimental developments, but also a large volume theoretical and computational studies addressing multi-component nonlinear Schrödinger models localized structures that they support. We focus on prototypical structures, namely dark-bright dark-dark solitons. Although our will be one-dimensional, two-component Hamiltonian models, discuss variants, including three (or more)-component higher-dimensional states, as well...

We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor $(F=1)$ Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system three coupled Gross-Pitaevskii equations (GPEs) to an integrable Yajima-Oikawa system. In this way, obtain approximate solutions for small-amplitude dark-dark-bright and bright-bright-dark types, terms ${m}_{F}=+1,\ensuremath{-}1,0$ components, respectively. By means numerical...

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by fact that matter-wave may naturally form such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we soliton interactions show well-separated (i.e., ones undergo a collision with relatively low velocities) can be analyzed means particle-like equations motion. The latter take into regard repulsion between (via an effective repulsive...

A quantized vortex dipole is the simplest molecule, comprising two countercirculating lines in a superfluid. Although dipoles are endemic two-dimensional superfluids, precise details of their dynamics have remained largely unexplored. We present here several striking observations dilute-gas Bose-Einstein condensates, and develop vortex-particle model that generates line trajectories good agreement with experimental data. Interestingly, these diverse exhibit essentially identical...

Motivated by recent experimental results, we study beating dark–dark (DD) solitons as a prototypical coherent structure that emerges in two-component Bose–Einstein condensates. We showcase their connection to dark–bright via SO(2) rotation, and infer from it both intrinsic frequency of oscillation inside parabolic trap. identify them exact periodic orbits the Manakov limit equal inter- intra-species nonlinearity strengths with without trap persistence such states upon weak deviations this...

We study the dynamics of small vortex clusters with a few (2-4) corotating vortices in Bose-Einstein condensates by means experiments, numerical computations, and theoretical analysis. All these approaches corroborate counterintuitive presence dynamical instability symmetric configurations. The arises as pitchfork bifurcation at sufficiently large values system angular momentum that induces emergence stabilization asymmetric rotating latter are quantified model observed experiments. is...

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been focus intense research efforts, extension to three components has never attempted experiments. Here, we experimentally demonstrate existence robust dark-bright-bright (DBB) dark-dark-bright a multicomponent F=1 condensate. We observe lifetimes on order hundreds milliseconds these Our...

We unravel the existence and stability properties of dark soliton solutions as they extend from regime trapped quantum droplets towards Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a phase-plane analysis, we identify regimes different types subsequently examine possibility black gray solitons kink-type structures this system. Moreover, employ Landau dynamics approach to extract an analytical estimate oscillation frequency single relevant extended Gross--Pitaevskii...

The modulational instability of the nonlinear Schr\"odinger (NLS) equation is examined in case with a quadratic external potential. This study motivated by recent experimental results context matter waves Bose-Einstein condensates (BECs). theoretical analysis invokes lens-type transformation that converts Gross-Pitaevskii into modified NLS without explicit spatial dependence. suggests particular interest specific time-varying potential $[\ensuremath{\sim}{(t+t}^{*}{)}^{\ensuremath{-}2}].$ We...

We investigate the dynamics of matter-wave solitons in presence a spatially varying atomic scattering length and nonlinearity. The bright dark solitary waves is studied using corresponding Gross-Pitaevskii equation. numerical results are shown to be very good agreement with predictions effective equations motion derived by adiabatic perturbation theory. dependent nonlinearity leads gravitational potential that allows influence both fundamental as well higher order solitons.

We report the first observation of stationary necklacelike solitons. Such necklace structures were realized when a high-order vortex beam was launched appropriately into two-dimensional optically induced photonic lattice. Our theoretical results obtained with continuous and discrete models show that solitons resulting from charge-4 have pi phase difference between adjacent "pearls" are formed in an octagon shape. Their stability region is identified.