Closed Loop Solitons and Sigma Functions: Classical and Quantized Elasticas with Genera One and Two

Abstract

Closed loop solitons in a plane, whose curvatures obey the modified Korteweg-de Vries equation, were investigated. It was shown that their tangential vectors are expressed by ratio of Weierstrass sigma functions for genus one case and ratio of Baker's sigma functions for the genus two case. This study is closely related to classical and quantized elastica problems.

AMS-Tex Use 12 pages

References in corpus (3)

• 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

Cited by in corpus (4)

• Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
• Multi-Dimensional Sigma-Functions
• Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica
• Hyperelliptic Solutions of Modified Korteweg-de Vries Equation of Genus g: Essentials of Miura Transformation