Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies
著者
書誌事項
Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies
（Memoirs of the American Mathematical Society, no. 641）
American Mathematical Society, 1998
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注記
"September 1998, volume 135, number 641 (first of 5 numbers)"
Includes bibliographical references (p. 76-79)
内容説明・目次
内容説明
In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. It features a simple and unified treatment of the topic. It has self-contained development. There are novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.
目次
Introduction The Toda hierarchy, recursion relations, and hyperelliptic curves The stationary Baker-Akhiezer function Spectral theory for finite-gap Jacobi operators Quasi-periodic finite-gap solutions of the stationary Toda hierarchy Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy Spectral theory for finite-gap Dirac-type difference operators Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy Hyperelliptic curves of the Toda-type and theta functions Periodic Jacobi operators Examples, $g-0,1$ Acknowledgments Bibliography.
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