Toroidal solitons in magnetic oxides,Bose-Einstein condensates,and other media

We consider toroidal soliton solutions in a number of nonlinear models of field theory (Skyrme, Faddeev, and Higgs models). Such models are used in various areas of solid-state chemistry and physics, chemical physics, astrophysics, and plasma chemistry and physics. The stability of toroidal solitons is shown to have a topological nature. We examine different methods of generating a nonlinear contribution to the Lagrangian in order to insure stability of the torus to collapse. Using the Faddeev and Skyrme models, we analyze the toroidal ordering in Bose-Einstein condensates of ²³Na, ³⁹K, and ⁸⁷Rb alkali-metal atoms, the toroidal structures recently found in the magnetic oxides BiFeO₃ and GaFeO₃, and potential applications of such structures in spintronics. In addition, we address several critical issues in the chemistry and physics of solitons with high topological charges.