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 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...

Fluids subjected to suitable forcing will exhibit turbulence, with characteristics strongly affected by the fluid's physical properties and dimensionality. In this work, we explore two-dimensional (2D) quantum turbulence in an oblate Bose-Einstein condensate confined annular trapping potential. Experimentally, find conditions for which small-scale stirring of generates disordered 2D vortex distributions that dissipatively evolve toward persistent currents, indicating energy transport from...

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...

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 provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. use the propagation highly nonlinear solitary waves as diagnostic tool and develop optimization schemes that allow one to compute relevant exponents prefactors terms equations motion. thereby propose quantitatively-accurate extension Hertzian model encompasses via discrete Laplacian velocities. Experiments computations with steel, brass, polytetrafluoroethylene reveal {\em common}...

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...

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...

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...

Non-Hermitian lattices with nonreciprocal couplings under open boundary conditions are known to possess linear modes exponentially localized on one edge of the chain. This phenomenon, dubbed non-Hermitian skin effect, induces all input waves in linearized limit system unidirectionally propagate toward system's preferred boundary. Here we investigate fate effect presence Kerr-type nonlinearity within well-established Hatano-Nelson lattice model. Our method is probe nonlinear stationary which...

We present experimental results and a systematic theoretical analysis of dark-br ight soliton interactions multiple-dark-bright complexes in atomic t wo-component Bose-Einstein condensates. study analytically the b etween two-dark-bright solitons homogeneous condensate and, then, extend ou r considerations to presence trap. An effective equation motion is derived for dark-bright center existence stability stationary states illustrated (with bright components being either in- or...

We study possibilities to suppress the transverse modulational instability (MI) of dark-soliton stripes in two-dimensional Bose-Einstein condensates (BEC's) and self-defocusing bulk optical waveguides by means quasi-one-dimensional structures. Adding an external repulsive barrier potential (which can be induced BEC a laser sheet, or embedded plate optics), we demonstrate that it is possible reduce MI wave number band, even render stripe completely stable. Using this method, control vortex...

In this work we study spherical shell dark soliton states in three-dimensional atomic Bose-Einstein condensates. Their symmetry is exploited order to analyze their existence, as well that of topologically charged variants the structures, and, importantly, identify linear stability Bogolyubov-de Gennes spectrum. We compare our effective 1D and 2D cylindrical computations with full 3D numerics. An important conclusion such solitons can be stable sufficiently close limit isotropic condensates...

We explore the dynamics and interactions of multiple bright droplets bubbles, as well kinks with antikinks, in extended one-dimensional Gross–Pitaevskii model including Lee–Huang–Yang correction. Existence regions are identified for bubbles terms their chemical potential, verifying stability exposing instability bubbles. The limiting case droplet family is a stable kink. between demonstrate in-phase (out-of-phase) attraction (repulsion), so-called Manton’s method explicating observed...

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation strength transverse confinement. We offer a fully analytical explanation observed parametric resonance, based Mathieu-type analysis non-polynomial Schr\"odinger equation. The theoretical prediction for pattern periodicity versus driving frequency is directly compared experimental data,...

In the present work, we offer a unifying perspective between dark soliton stripe and vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in context of quasi-two-dimensional Bose-Einstein condensates. particular, illustrate multivortex with vortices along (former) sequentially bifurcate from latter state supercritical pitchfork manner. Each additional bifurcation adds an extra mode to instability configuration; moreover, bifurcating inherit stability...

Consider a lower-dimensional solitonic structure embedded in higher-dimensional space, e.g., 1D dark soliton 2D ring spherical shell 3D etc. By extending the Landau dynamics approach [Phys. Rev. Lett. 93, 240403 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.240403], we show that it is possible to capture transverse dynamical modes (the "Kelvin modes") of undulation this "soliton filament" within space. These are stability or instability and ones potentially responsible for breakup into...

We study experimentally and theoretically the dynamics of apparent dark soliton stripes in an elongated Bose-Einstein condensate. show that for trapping strengths corresponding to our experimental setup, transverse confinement along one tight directions is not strong enough arrest formation solitonic vortices or vortex rings. These rings, when integrated direction, appear as longitudinal direction thereby hiding their true character. The latter significantly modifies interaction during...

Quantum vortices, the quantized version of classical play a prominent role in superfluid and superconductor phase transitions. However, their exploration at particle level open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions resonant polariton fluid created solid-state microcavity. By tracking vortices on picosecond time scales, reveal nonlinearity, as well density gradients, driving rotational dynamics. Such effects are also...