A Spectral Theory For Simply Periodic Solutions Of The Sinh Gordon Equation
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.
- Condition: --
HPB condition ratings
- New: Item is brand new, unused and unmarked, in flawless condition.
- Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
- Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
- Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
- Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
- Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
- Format: Paperback
- Sold by: --
- Language: English
- Publisher: Springer Nature
- ISBN-13: 9783030012755
- ISBN: 3030012751
- Publication Year: 2018