Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-10-13
Eur.Phys.J.C42:461-473,2005
Physics
High Energy Physics
High Energy Physics - Theory
31 pages, 21 figures; final version accepted in Eur. Phys. J. C
Scientific paper
10.1140/epjc/s2005-02300-4
The complex eikonal equation in $(3+1)$ dimensions is investigated. It is shown that this equation generates many multi soliton configurations with arbitrary value of the Hopf index. In general, these eikonal hopfions do not have the toroidal symmetry. For example, a hopfion with topology of the trefoil knot is found. Moreover, we argue that such solitons might be helpful in construction of approximated analytical knotted solutions of the Faddeev-Niemi model.
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