03581nam 22006615 450 991030345630332120200706230134.03-030-01276-X10.1007/978-3-030-01276-2(CKB)4100000007204674(DE-He213)978-3-030-01276-2(MiAaPQ)EBC6295783(PPN)232961484(EXLCZ)99410000000720467420181205d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierA Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation /by Sebastian Klein1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (VIII, 334 p. 7 illus.) Lecture Notes in Mathematics,0075-8434 ;22293-030-01275-1 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. .Lecture Notes in Mathematics,0075-8434 ;2229Partial differential equationsDifferential geometryFunctional analysisFunctions of complex variablesDifferential equationsPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Functions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Partial 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.515.353515.353Klein Sebastianauthttp://id.loc.gov/vocabulary/relators/aut760812MiAaPQMiAaPQMiAaPQBOOK9910303456303321Spectral theory for simply periodic solutions of the Sinh-Gordon equation1539995UNINA