Knots, Braids and Hedgehogs from the Eikonal Equation

Details Knots, Braids and Hedgehogs from the Eikonal Equation Knots, Braids and Hedgehogs from the Eikonal Equation

2005-06-14

arxiv.org/abs/math-ph/0506035v1

Mod.Phys.Lett. A20 (2005) 1135-1146

Physics

Mathematical Physics

15 pages, 5 figures

Scientific paper

10.1142/S0217732305017330

The complex eikonal equation in the three space dimensions is considered. We show that apart from the recently found torus knots this equation can also generate other topological configurations with a non-trivial value of the $\pi_2(S^2)$ index: braided open strings as well as hedgehogs. In particular, cylindric strings i.e. string solutions located on a cylinder with a constant radius are found. Moreover, solutions describing strings lying on an arbitrary surface topologically equivalent to cylinder are presented. We discus them in the context of the eikonal knots. The physical importance of the results originates in the fact that the eikonal knots have been recently used to approximate the Faddeev-Niemi hopfions.

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