Knots in magnets

Abstract:
Topological solitons, i.e. stable, particle-like objects with a non-vanishing topogical charge occur in various contexts of the theoretical physics. For example, hopfions i.e. topological solitons with the non-trivial Hopf index have been recently analyzed in a connection with the non-perturbative regime of the gluodynamics [1]. It has been suggested by Faddeev and Niemi that particles built only of the gauge field, so-called glueballs, can be described as knotted solitons with a non-vanishing value of the Hopf index. In this work, the (3+1)-dimensional generalized Landau-Lifshitz equation is considered. It is shown that this equation admits many types knotted configurations which correspond an arbitrary value Hopf index. The results reported are based on the article [2].

1. Wereszczynski A. Knots, Braids and Hedgehogs from the Eikonal Equation. Mod. Phys. Lett., A20, 1135-1146 (2005).
2. Myrzakulov R. et al. Magnetic knots and links. Vestnik al-Farabi KazNU. Ser. fiz., N20, 12-21 (2005).