A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple _quantum droplets_ in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and _fractional diffraction_, and the prediction of stable 3D _vortex solitons_ in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [B.A. Malomed, Multidimensional soliton systems. Adv. Phys. 9(1) (2024), pp. 2301592] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose–Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as solitons supported by thermal nonlinearity in optical glasses, and orientational nonlinearity, which affects light propagation in liquid crystals) are well known, and have been properly reviewed in the literature, therefore the respective models are outlined in the present review in a brief form. Some other studies, such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have started more recently, therefore it will be relevant to review them in detail when more results will be accumulated; for this reason, the present article provides a short outline of the latter topic. The main part of the article is a summary of results obtained for two-dimensional solitons in specific nonlocal nonlinear models originating in studies of Bose–Einstein condensates (BECs), which are sufficiently mature but have not yet been reviewed previously (some results for three-dimensional solitons are briefly mentioned too). These are, in particular, anisotropic quasi-2D solitons supported by long-range dipole-dipole interactions in a condensate of magnetic atoms and giant vortex solitons (which are stable for high values of the winding number), as well as 2D vortex solitons of the latter type moving with self-acceleration. The vortex solitons are states of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a microwave field that couples the two atomic states. The shape, stability, and dynamics of the solitons in such systems are strongly affected by their symmetry. Some other topics are included in the review in a brief form. This review uses the “Harvard style” of referring to the bibliography.
The study of soliton-like states in systems with nonlocal nonlinearity is a traditional topic in optics and related areas. Some results obtained in these studies (such as solitons supported by thermal nonlinearity in optical glasses and orientational nonlinearity that affects light propagation in liquid crystals) are well known and have been properly reviewed in the literature; therefore, the respective models are outlined in the present chapter in a brief form. Some other studies such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have also been started more recently; therefore, it should be relevant to review them in detail when more results will be accumulated and this chapter includes a short outline of the latter topic. After providing an introduction to the general area of nonlocal nonlinearities, the chapter offers a summary of results obtained for multidimensional solitons in some specific nonlocal nonlinear models originating in studies of BEC, which are sufficiently mature but have not been reviewed previously. These are anisotropic quasi-2D solitons supported by long-range dipole–dipole interactions in a condensate of magnetic atoms [Tikhonenkov et al., Phys. Rev. Lett. 100, 090406(2008a)] and giant vortex solitons, which are stable for high values of the winding number [Qin et al., Phys. Rev. A 94, 053611 (2016)], as well as 2D vortex solitons moving with self-acceleration [Qin et al., Phys. Rev. A 99, 023610 (2019)]. These are solitons of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a resonant microwave field which couples the two atomic states.
We review the state of the art and recently obtained theoretical and experimental results for two- and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates (BECs), and other fields - in particular, liquid crystals. The central challenge is avoiding the trend of 2D and 3D solitary states supported by the ubiquitous cubic nonlinearity to be strongly unstable - a property far less present in one-dimensional systems. Many possibilities for the stabilization of multi-dimensional states have been theoretically proposed over the years. Most strategies involve non-cubic nonlinearities or using different sorts of potentials, including periodic ones. New important avenues have arisen recently in systems based on two-component BEC with spin-orbit coupling, which have been predicted to support stable 2D and metastable 3D solitons. An important recent breakthrough is the creation of 3D quantum droplets. These are self-sustained states existing in two-component BECs, which are stabilized by the presence of Lee-Hung-Yang quantum fluctuations around the underlying mean-field states. By and large, multi-dimensional geometries afford unique opportunities to explore the existence of complex self-sustained states, including topologically rich ones, which by their very nature are not possible in one-dimensional geometries. In addition to vortex solitons, these are hopfions, skyrmions, and hybrid vortex-antivortex complexes, which have been predicted in different models. Here we review recent landmark findings in this field and outline outstanding open challenges.
This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison with commonly known one-dimensional solitons, which are, normally, stable modes, a challenging problem is the propensity of 2D and 3D solitons to instability, caused by the occurrence of the critical or supercritical wave collapse (catastrophic self-compression) in the same spatial dimension. A remarkable feature of multidimensional solitons is their ability to carry vorticity; however, 2D vortex rings and 3D vortex tori are subject to strong splitting instability. Therefore, it is natural to categorize the basic results according to physically relevant settings which make it possible to maintain stability of fundamental (non-topological) and vortex solitons against the collapse and splitting, respectively. The present review is focused on schemes that were recently elaborated in terms of Bose-Einstein condensates and similar photonic setups. These are two-component systems with spin-orbit coupling, and ones stabilized by the beyond-mean-field Lee-Huang-Yang effect. The latter setting has been implemented experimentally, giving rise to stable self-trapped quasi-2D and 3D "quantum droplets".