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

2001/08/31 by Shigeki Matsutani · 2 citations
Mathematics · Physics and Astronomy · #math-ph #math.DG #math.MP #nlin.SI

paper · pdf · doi:10.1016/s0393-0440(02)00017-7

AMS-Tex, 14 pages

arxiv created 2001/12/24 · arxiv updated 2009/11/30

Abstract

In the previous work (J. Geom. Phys. \bf39 (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 y² = f(x) with genus g.

Cited by

• Geometric, algebraic and analytic properties of hyperelliptic al_ab function of genus g
• Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus g