The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions

Details The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions

2012-04-19

arxiv.org/abs/1204.4240v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

45 pages

Scientific paper

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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