Relations in a Loop Soliton as a Quantized Elastica

TL;DR

This paper explores the mathematical relations of loop solitons modeled as quantized elastica, building on previous work that connected hyperelliptic solutions to elastica theory.

Contribution

It introduces new functional relations in loop solitons interpreted as quantized elastica, extending prior hyperelliptic solution analysis.

Findings

Derived functional relations for loop solitons as quantized elastica

Extended understanding of the mathematical structure of loop solitons

Connected hyperelliptic solutions to elastica theory

Abstract

In the previous article (J. Geom. Phys. {\bf 43} (2002) 146), we show the hyperelliptic solutions of a loop soliton as a study of a quantized elastica. This article gives some functional relations in a loop soliton as a quantized elastica.