Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Details Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

1997-05-29

arxiv.org/abs/solv-int/9705019v1

Memoirs of the Amer. Math. Soc. 135/641, 1998

Mathematics

Spectral Theory

LaTeX, to appear in Memoirs of the Amer. Math. Soc

Scientific paper

Combining algebro-geometric methods and factorization techniques for finite difference expressions we provide a complete and self-contained treatment of all real-valued quasi-periodic finite-gap solutions of both the Toda and Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we employ particular commutation methods in connection with Miura-type transformations which enable us to transfer whole classes of solutions (such as finite-gap solutions) from the Toda hierarchy to its modified counterpart, the Kac-van Moerbeke hierarchy, and vice versa.

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