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

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

2000-08-20

arxiv.org/abs/math/0008153v3

Mathematics

Differential Geometry

AMS-Tex Use 12 pages

Scientific paper

10.1016/S0393-0440(00)00074-7

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.

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