2,173 research outputs found
Closed Loop Solitons and Sigma Functions: Classical and Quantized Elasticas with Genera One and Two
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.Comment: AMS-Tex Use 12 page
Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica
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 with genus .Comment: AMS-Tex, 14 page
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