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200 12$aA Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation /$fby Sebastian Klein
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (VIII, 334 p. 7 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2229
311   $a3-030-01275-1 
330   $aThis book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces. .
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2229
606   $aPartial differential equations
606   $aDifferential geometry
606   $aFunctional analysis
606   $aFunctions of complex variables
606   $aDifferential equations
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
615  0$aPartial differential equations.
615  0$aDifferential geometry.
615  0$aFunctional analysis.
615  0$aFunctions of complex variables.
615  0$aDifferential equations.
615 14$aPartial Differential Equations.
615 24$aDifferential Geometry.
615 24$aFunctional Analysis.
615 24$aFunctions of a Complex Variable.
615 24$aOrdinary Differential Equations.
676   $a515.353
676   $a515.353
700   $aKlein$b Sebastian$4aut$4http://id.loc.gov/vocabulary/relators/aut$0760812
801  0$bMiAaPQ
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906   $aBOOK
912   $a9910303456303321
996   $aSpectral theory for simply periodic solutions of the Sinh-Gordon equation$91539995
997   $aUNINA