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

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 087/5 ( reviews)

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Book Synopsis Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by : Wolfgang Bulla

Download or read book Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies written by Wolfgang Bulla. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: 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. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

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

2014-09-11 MATHEMATICS
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Release : 2014-09-11
Genre : MATHEMATICS
Kind : eBook
Book Rating : 303/5 ( reviews)

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Book Synopsis Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-Van Moerbeke Hierarchies by : Wolfgang Bulla

Download or read book Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-Van Moerbeke Hierarchies written by Wolfgang Bulla. This book was released on 2014-09-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 065/5 ( reviews)

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Book Synopsis (m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions by : Fritz Gesztesy

Download or read book (m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions written by Fritz Gesztesy. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators. We then illustrate Miura's transformation, which maps solutions of the mKdV into solutions of the KdV. We then give a general overview of the concept of soliton solutions relative to general backgrounds, and of the single and double commutation methods. Finally, we present the main results of the article. To avoid the clutter of too many technical details, the paper is organized in four sections and five appendices.

Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

2008-09-04 Mathematics
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Release : 2008-09-04
Genre : Mathematics
Kind : eBook
Book Rating : 778/5 ( reviews)

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Book Synopsis Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models by : Fritz Gesztesy

Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models written by Fritz Gesztesy. This book was released on 2008-09-04. Available in PDF, EPUB and Kindle. Book excerpt: As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

Modern Analysis and Applications

2009-08-29 Mathematics
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Release : 2009-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 21X/5 ( reviews)

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Book Synopsis Modern Analysis and Applications by : Vadim Adamyan

Download or read book Modern Analysis and Applications written by Vadim Adamyan. This book was released on 2009-08-29. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

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