Multidimensional Solitons in Nonlocal Media

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.