Algebro-geometric Quasi-periodic Finite-gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Buch | Softcover

79 Seiten

1998
American Mathematical Society (Verlag)
9780821808085 (ISBN)

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Offers 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. This work offers an approach that utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations.

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.

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.

Erscheint lt. Verlag	30.8.1998
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-13	9780821808085 / 9780821808085
Zustand	Neuware