Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica

Abstract

In the previous work (J. Geom. Phys. {\bf{39}} (2001) 50-61), the closed loop solitons in a plane, \it i.e., loops whose curvatures obey the modified Korteweg-de Vries equations, were investigated for the case related to algebraic curves with genera one and two. This article is a generalization of the previous article to those of hyperelliptic curves with general genera. It was proved that the tangential angle of loop soliton is expressed by the Weierstrass hyperelliptic al function for a given hyperelliptic curve $y^2=f(x)$ with genus $g$.

AMS-Tex, 14 pages

References in corpus (4)

• Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
• Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-
• Statistical Mechanics of Non-stretching Elastica in Three Dimensional Space
• Closed Loop Solitons and Sigma Functions: Classical and Quantized Elasticas with Genera One and Two

Cited by in corpus (6)

• Multi-Dimensional Sigma-Functions
• An algebro-geometric model for the shape of supercoiled DNA
• Wannier functions for quasi-periodic finite-gap potentials
• From Euler's elastica to the mKdV hierarchy, through the Faber polynomials
• Reality Conditions of Loop Solitons Genus g: Hyperelliptic am Functions
• Relations in a Loop Soliton as a Quantized Elastica