Abstract
We review our work on topological solitons in the Faddeev‐Skyrme model. This model describes the dynamics of a three‐dimensional unit vector‐field in the three‐dimensional space and the conserved topological quantity is the Hopf charge. The main question here is the shape (knottedness) of the minimum energy state for a given Hopf charge. It can be found by dissipative dynamics from a suitable initial state. For charges>3 the final states are not simple but consist of linked knots and the deformation process leading to them is interesting. We have also studied the same question for vortices in a periodic box. If the box is periodic in all directions the Hopf charge is no longer conserved. The results have been obtained in collaboration with J. Jäykkä and P. Salo.
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