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Author:   Sebastian Klein
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2018
Volume:   2229
Weight:   0.528kg
ISBN:  

9783030012755

ISBN 10:   3030012751
Pages:   334
Publication Date:   06 December 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

- Part I Spectral Data. - Introduction. - Minimal Immersions into the 3-Sphere and the Sinh-Gordon Equation. - Spectral Data for Simply Periodic Solutions of the Sinh-Gordon Equation. - Part II The Asymptotic Behavior of the Spectral Data. - The Vacuum Solution. - The Basic Asymptotic of the Monodromy. - Basic Behavior of the Spectral Data. - The Fourier Asymptotic of the Monodromy. - The Consequences of the Fourier Asymptotic for the Spectral Data. - Part III The Inverse Problem for the Monodromy. - Asymptotic Spaces of Holomorphic Functions. - Interpolating Holomorphic Functions. - Final Description of the Asymptotic of the Monodromy. - Non-special Divisors and the Inverse Problem for the Monodromy. - Part IV The Inverse Problem for Periodic Potentials (Cauchy Data). - Divisors of Finite Type. - Darboux Coordinates for the Space of Potentials. - The Inverse Problem for Cauchy Data Along the Real Line. - Part V The Jacobi Variety of the Spectral Curve. - Estimate of Certain Integrals. - Asymptotic Behavior of 1-Forms on the Spectral Curve. - Construction of the Jacobi Variety for the Spectral Curve. - The Jacobi Variety and Translations of the Potential. - Asymptotics of Spectral Data for Potentials on a Horizontal Strip. - Perspectives.

Reviews

“The book is useful for specialists studying periodic solutions to integrable nonlinear partial differential equations.” (Dmitry E. Pelinovsky, Mathematical Reviews, October, 2019)

The book is useful for specialists studying periodic solutions to integrable nonlinear partial differential equations. (Dmitry E. Pelinovsky, Mathematical Reviews, October, 2019)

Author Information

Sebastian Klein obtained his doctorate at the Universität zu Köln in 2005 in differential geometry. After a 2-year postdoc stay at University College Cork (UCC), he moved to Universität Mannheim in 2008. Here his research focus expanded into geometric analysis and integrable systems. He was a temporary lecturer at UCC in 2016-17, and is at the moment a Privatdozent in Mannheim.

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