Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers - Aratyn, H.; Ferreira, L. A.; Zimerman, A. H. (American Physical Soc, 1999)
In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero 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 explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.