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Spectral Data for Simply Periodic Solutions of the Sinh-Gordon Equation

  • Sebastian Klein
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2229)

Abstract

We now suppose that a simply periodic solution \(u: X \to \mathbb {C}\) of the sinh-Gordon equation \(\triangle u + \sinh (u)=0\) on an (open or closed) domain \(X \subset \mathbb {C}\) is given. Without loss of generality, we suppose that 0 ∈ X and that \(1\in \mathbb {C}\) is the period of u.

References

  1. [deJ-P]
    T. de Jong, G. Pfister, Local Analytic Geometry (Vieweg, Braunschweig 2000)CrossRefGoogle Scholar
  2. [Har-2]
    R. Hartshorne, Generalized divisors on Gorenstein curves and a theorem of Noether. J. Math. Kyoto Univ. 26, 375–386 (1986)MathSciNetCrossRefGoogle Scholar
  3. [Hi]
    N.J. Hitchin, Harmonic maps from a 2-torus to the 3-sphere. J. Differ. Geom. 31, 627–710 (1990)MathSciNetCrossRefGoogle Scholar
  4. [Kl-L-S-S]
    S. Klein, E. Lübcke, M. Schmidt, T. Simon, Singular curves and Baker-Akhiezer functions, submitted for publication, arXiv:1609.07011 (2016)Google Scholar
  5. [Pö-T]
    J. Pöschel, E. Trubowitz, Inverse Spectral Theory (Academic Press, London, 1987)zbMATHGoogle Scholar
  6. [Sch]
    M. Schmidt, Integrable Systems and Riemann Surfaces of Infinite Genus (American Mathematical Society, Providence, 1996)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sebastian Klein
    • 1
  1. 1.School of Business Informatics & MathematicsUniversity of MannheimMannheimGermany

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