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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation
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Catalogue Information
Field name
Details
Dewey Class
516.36
Title
A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation (EB) / Sebastian Klein
Author
Klein, Sebastian
Publication
Cham : Springer International Publishing AG , 2018
Physical Details
1 online resource
Series
Lecture Notes in Mathematics
; 2229
ISBN
9783030012762
Summary Note
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.:
Mode of acces to digital resource
Digital book Cham Springer International Publishing, 2018 Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF (3450 KB) format and ePub (ePub,3526 KB)
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
https://doi.org/10.1007/978-3-030-01276-2
Links to Related Works
Subject References:
Constant Mean Curvature Surfaces
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Integrable systems
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Sinh-Gordon Equation
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Spectral theory (Mathematics)
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Authors:
Klein, Sebastian
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Series:
Lecture Notes in Mathematics
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Classification:
516.36
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516.36 (DDC 23)
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