Exact static soliton solutions of (3+1)-dimensional integrable theory withnonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (stat ic, soliton solutions with nonzero Hopf topological charges) within the rec ently proposed (3 + 1)-dimensional, integrable, and relativistically invari ant 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 t he soliton's finite energy. The Hopfions are explicitly constructed in term s of the toroidal coordinates and shown to have a form of linked closed vor tices.