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arXiv · hep-th/9905079

Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers

H. Aratyn·L. A. Ferreira·A. H. Zimerman
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Abstract

In this paper we construct explicitly an infinite number of Hopfions (static, soliton solutions with non-zero Hopf topological charges) within the recently proposed 3+1-dimensional, integrable and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are constructed explicitly in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

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H. Aratyn, L. A. Ferreira, A. H. Zimerman. 1999-05-11. Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers. https://doi.org/10.1103/physrevlett.83.1723

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