1.

Record Nr.

UNINA9910303456303321

Autore

Klein Sebastian

Titolo

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

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018

ISBN

3-030-01276-X

Edizione

[1st ed. 2018.]

Descrizione fisica

1 online resource (VIII, 334 p. 7 illus.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2229

Disciplina

515.353

Soggetti

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

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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. .