Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 4, pp. 452-509   https://doi.org/10.15407/mag14.04.452     ( to contents , go back )
https://doi.org/10.15407/mag14.04.452

On Spectral Properties of the L Operator in the Lax Pair of the sine-Gordon Equation

Thomas Kappeler

Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
E-mail: thomas.kappeler@math.uzh.ch

Yannick Widmer

Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
E-mail: Yannick.Widmer@math.uzh.ch

Received February 15, 2018.

To Professor Vladimir Aleksandrovich Marchenko on the occasion of his ninety fifth birthday

Abstract

We analyze the periodic spectrum of the L operator in the Lax pair of the sine-Gordon equation in terms of the regularity of the potential.

Mathematics Subject Classification 2000: 37K10, 35Q55.
Key words: sine-Gordon equation, sinh-Gordon equation, Lax pair, decay properties of gap lengths.

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