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＜電子ブック＞
A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation / by Sebastian Klein
(Lecture Notes in Mathematics. ISSN:16179692 ; 2229)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	VIII, 334 p. 7 illus : online resource
著者標目	*Klein, Sebastian author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Geometry, Differential LCSH:Functional analysis LCSH:Functions of complex variables FREE:Differential Equations FREE:Differential Geometry FREE:Functional Analysis FREE:Functions of a Complex Variable
一般注記	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. HTTP:URL=https://doi.org/10.1007/978-3-030-01276-2

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