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arXiv · 1204.4240

The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy

Peng Zhao·Engui Fan·Yu Hou
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Abstract

We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperelliptic curve $\mathcal{K}_p$ associated with the Burchnall-Chaundy polynomial, Dubrovin-type equations for auxiliary divisors and associated trace formulas. With the help of a foundamental meromorphic function $\phi$, Baker-Akhiezer vector $\Psi$ on $\mathcal{K}_p$, the complex-valued algebro-geometric solutions of RT hierarchy are derived.

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Peng Zhao, Engui Fan, Yu Hou. 2012-04-19. The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy. https://doi.org/10.1016/j.chaos.2013.05.012

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