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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation / by Sebastian Klein.
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View onlineMath/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2384 2385-2386,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Klein, Sebastian (Mathematician), author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2229.
- Lecture Notes in Mathematics, 0075-8434 ; 2229
- Language:
- English
- Subjects (All):
- Differential equations, Partial.
- Global 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.
- Local Subjects:
- Partial Differential Equations.
- Differential Geometry.
- Functional Analysis.
- Functions of a Complex Variable.
- Ordinary Differential Equations.
- Physical Description:
- 1 online resource (VIII, 334 pages 7 illustrations).
- Contained In:
- Springer eBooks
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2018.
- System Details:
- text file PDF
- Summary:
- 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, id est 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. .
- Other Format:
- Printed edition:
- ISBN:
- 9783030012762
- Access Restriction:
- Restricted for use by site license.
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