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The Lie Group Structure of Elliptic/Hyperelliptic Functions
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
We consider the generalized dual transformation for elliptic/hyperelliptic functions up to genus three. For the genus one case, from the algebraic addition formula, we deduce…
The Half-period Addition Formulae for Genus Two Hyperelliptic Functions and the Sp(4,) Lie Group Structure
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
In the previous study, by using the two-flows Kowalevski top, we have demonstrated that the genus two hyperelliptic functions provide the Sp(4,)/ SO(3,2) L…
Two Flows Kowalevski Top as the Full Genus Two Jacobi's Inversion Problem and Sp(4,) Lie Group Structure
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
By using the first and the second flows of the Kowalevski top, we can make the Kowalevski top into the two flows Kowalevski top, which has two time variales. Then we show that equa…
Differential Equations of Genus Four Hyperelliptic Functions
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
In order to find higher dimensional integrable models, we study differential equations of hyperelliptic functions up to genus four. For genus two, differential equations of h…
Elliptic Solutions for Higher Order KdV Equations
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
We study higher order KdV equations from the GL(2,) SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth or…
Common Hirota Form Bäcklund Transformation for the Unified Soliton System
Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka
We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) GL(2,) Möbius group point of view, which might be a keystone to exactly solve so…