Reality conditions of loop solitons genus $g$: hyperelliptic am functions

Abstract

This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic curve. We also compute winding numbers of loop solitons.

Keywords

• Loop soliton
• elastica
• reality condition
• hyperelliptic functions