A spectral theory for simply periodic solutions of the Sinh-Gordon equation / Sebastian Klein.

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A spectral theory for simply periodic solutions of the Sinh-Gordon equation / Sebastian Klein.

9783030012762 (electronic book)
303001276X (electronic book)
9783030012755 print

Cham, Switzerland : Springer, [2018]

English

1 online resource

10.1007/978-3-030-01276-2 doi

QA371 .K44 2018

515.353

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.

Includes bibliographical references and index.

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Description based on online resource; title from digital title page (viewed on January 23, 2019).

Lecture notes in mathematics (Springer-Verlag) ; 2229.

Print version: 9783030012755

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