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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation / / by Sebastian Klein



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Autore: Klein Sebastian Visualizza persona
Titolo: A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation / / by Sebastian Klein Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
Edizione: 1st ed. 2018.
Descrizione fisica: 1 online resource (VIII, 334 p. 7 illus.)
Disciplina: 515.353
Soggetto topico: Partial differential equations
Differential geometry
Functional analysis
Functions of complex variables
Differential equations
Partial Differential Equations
Differential Geometry
Functional Analysis
Functions of a Complex Variable
Ordinary Differential Equations
Sommario/riassunto: 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. .
Titolo autorizzato: Spectral theory for simply periodic solutions of the Sinh-Gordon equation  Visualizza cluster
ISBN: 3-030-01276-X
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910303456303321
Lo trovi qui: Univ. Federico II
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Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2229