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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation by Sebastian Klein
A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation by Sebastian Klein
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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation

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Description

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.  Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space.  Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data.  Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u.  The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.   

Author Biography:

Sebastian Klein obtained his doctorate at the Universit�t zu K�ln in 2005 in differential geometry. After a 2-year postdoc stay at University College Cork (UCC), he moved to Universit�t 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.
Release date NZ
December 6th, 2018
Audience
  • Professional & Vocational
Edition
1st ed. 2018
Illustrations
7 Illustrations, black and white; VIII, 334 p. 7 illus.
Pages
334
ISBN-13
9783030012755
Product ID
28351808

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