Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models (Cambridge Studies in Advanced Mathematics)

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9780521753074: Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models (Cambridge Studies in Advanced Mathematics)
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This book is about algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions; also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary and time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces).

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Book Description:

The Korteweg-de Vries (KdV) equation, the AKNS equation, the nonlinear Schrödinger equation, the sine-Gordon equation, the Thirring system, and the Camassa-Holm equation are all completely integrable nonlinear partial differential equations that permit special classes of solutions. This book offers a detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions. It provides a rigorous and self-contained presentation at the graduate level. Background material is succinctly presented in appendices and detailed notes to each chapter, and an exhaustive bibliography enhances the main text.

About the Author:

Fritz Gesztesy is Professor of Mathematics at the University of Missouri, Columbia.

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9780521753081: Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models (Cambridge Studies in Advanced Mathematics)

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Publisher: Cambridge University Press, 2008
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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2016. Hardback. Condition: New. New. Language: English . Brand New Book ***** Print on Demand *****. The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text. Seller Inventory # APC9780521753074

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