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

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

2001-08-04

arxiv.org/abs/nlin/0108001v4

Nonlinear Sciences

Exactly Solvable and Integrable Systems

AMS-Tex, 14 pages

Scientific paper

10.1016/S0393-0440(02)00017-7

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 $g$.

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