paper

The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy

arXiv:1204.4240 · doi:10.1016/j.chaos.2013.05.012

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 $K_{p}$ associated with the Burchnall-Chaundy polynomial, Dubrovin-type equations for auxiliary divisors and associated trace formulas. With the help of a foundamental meromorphic function $I ¨ $ , Baker-Akhiezer vector $I^¨$ on $K_{p}$ , the complex-valued algebro-geometric solutions of RT hierarchy are derived.

49 pages. arXiv admin note: substantial text overlap with arXiv:nlin/0702058, arXiv:nlin/0611055 by other authors