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

W. Bulla; F. Gesztesy; H. Holden; G. Teschl

doi:10.1090/memo/0641

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

W. Bulla·F. Gesztesy·H. Holden·G. Teschl

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Abstract

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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W. Bulla, F. Gesztesy, H. Holden, G. Teschl. 1997-05-29. Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies. https://doi.org/10.1090/memo%2F0641

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