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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation/ by Sebastian Klein.
作者:	Klein, Sebastian.
面頁冊數:	VIII, 334 p. 7 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial differential equations. -
電子資源:	https://doi.org/10.1007/978-3-030-01276-2
ISBN:	9783030012762

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

A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation[electronic resource] /by Sebastian Klein. - 1st ed. 2018. - VIII, 334 p. 7 illus.online resource. - Lecture Notes in Mathematics,22290075-8434 ;. - Lecture Notes in Mathematics,2144.

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. .

ISBN: 9783030012762

Standard No.: 10.1007/978-3-030-01276-2doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

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