The Trefoil Soliton

Mathematics

David A. Singer¹ 

[1] Department of Mathematics, Applied Math & Statistics, Case Western Reserve University, Cleveland, OH 44106, USA;

关键词: trefoil;    filament equation;    soliton;   

DOI  :  10.3390/math10091512

来源: DOAJ

【 摘 要 】

The Kiepert trefoil is an algebraic curve with remarkable geometric and number theoretic properties. Ludwig Kiepert, generalizing ideas due to Serret and Liouville, determined that it could be parametrized by arc length in terms of elliptic functions. In this note, we observe some other properties of the curve. In particular, the curve is a special example of a buckled ring, and thus a solitary wave solution to the planar filament equation, evolving by rotation. It is also a solitary wave solution to a flow in the (three-dimensional) filament hierarchy, evolving by translation.

【 授权许可】

Unknown