On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics

Multidimensional solitons draw continuously renewed interest in many branches of physics, finding especially important realizations in nonlinear photonics (optics and plasmonics) and Bose?Einstein condensates (BECs). The solitons are classified as fundamental ones, which carry no topological structure, and various topological modes, including 2D and 3D solitons with embedded vorticity, and more sophisticated 3D states, such as hopfions. Indeed, the ubiquitous cubic self-attractive nonlinearity, which readily creates solitons, simultaneously gives rise to the critical and supercritical collapse, i.e., spontaneous formation of a singularity after a finite propagation distance or time, in the 2D and 3D geometries, respectively. The collapse destabilizes fundamental solitons, while their vortex solitons are subject to a still stronger splitting instability against perturbations breaking the axial symmetry of the vortices. The theoretical work in the area has been developing in many directions. One of them is the use of D-dimensional media with repulsive nonlinearity, whose local strength grows from the center to periphery.