A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation (Paperback, 1st ed. 2018)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2229
Release date:	December 2018
First published:	2018
Authors:	Sebastian Klein
Dimensions:	235 x 155 x 28mm (L x W x T)
Format:	Paperback
Pages:	334
Edition:	1st ed. 2018
ISBN-13:	978-3-03-001275-5
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	3-03-001275-1
Barcode:	9783030012755

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