| Summary: | 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, <i>anisotropic</i> quasi-2D solitons supported by long-range dipole-dipole interactions in a condensate of magnetic atoms and <i>giant vortex solitons</i> (which are stable for high values of the winding number), as well as 2D vortex solitons of the latter type <i>moving with self-acceleration</i>. 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.
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