Asymptotics of Spectral Data for Potentials on a Horizontal Strip

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


As a final result, we study the asymptotic behavior of the spectral data (Σ, D) corresponding to a simply periodic solution \(u: X \to \mathbb {C}\) of the sinh-Gordon equation defined on an entire horizontal strip \(X \subset \mathbb {C}\) with positive height. Because such a solution is real analytic on the interior of X, we expect a far better asymptotic for such spectral data than for the spectral data of Cauchy data potentials (u, uy) with only the weak requirements u ∈ W1, 2([0, 1]), uy ∈ L2([0, 1]) we have been using throughout most of the paper. More specifically, we expect both the distance of branch points ϰk,1 − ϰk,2 of the spectral curve Σ and the distance of the corresponding spectral divisor points to the branch points to fall off exponentially for k →±.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

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

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