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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation (Paperback, 1st ed. 2018)
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A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation (Paperback, 1st ed. 2018)
Series: Lecture Notes in Mathematics, 2229
Expected to ship within 10 - 15 working days
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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.
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