从程函方程看纽结、辫子和刺猬
Knots, Braids and Hedgehogs from the Eikonal Equation
摘要：
考虑三维空间中的复程函方程。我们发现，除了最近发现的环面结这个方程也可以产生其他拓扑结构的$π_2(S^2)$指数的非平凡值：编织开弦以及刺猬。特别地，我们找到了圆柱弦，即位于具有常数半径的圆柱上的弦解，并且给出了描述位于与圆柱拓扑等价的任意曲面上的弦的解。我们在程函结的背景下讨论它们。结果的物理重要性起源于程函结最近被用来近似Faddeev-Niemi hopfions的事实。
英文摘要：
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 $π_2(S^2)$ 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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