The Trefoil Soliton

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