Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
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E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA374.SPR FCT 98185 (Browse shelf) | 1 | Available |
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QA374.SPR FCT 98154 Solvability, regularity, and optimal control of boundary value problems for PDEs | QA374.SPR FCT 98158 Geometry of PDEs and related problems | QA374.SPR FCT 98183 Frontiers in PDE - constrained optimization | QA374.SPR FCT 98185 A spectral theory for simply periodic solutions of the Sinh-Gordon equation | QA374.SPR FCT 98194 Nonlinear elliptic partial differential equations | QA374.SPR FCT 98203 Asymptotics of elliptic and parabolic PDEs | QA374.SPR FCT 98216 PDE models for multi-agent phenomena |
Colocação: Online
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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