Maximal Densities of Finite-Gap Solutions of the Sine-Gordon Equation

Otis C. Wright III

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arXiv · 2607.03555

Maximal Densities of Finite-Gap Solutions of the Sine-Gordon Equation

Otis C. Wright III

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Abstract

We establish a sharp upper bound on the densities of finite-gap solutions of the sine-Gordon equation. The bound is derived directly from the finite-dimensional hierarchy, without explicit integration of the finite-gap solutions. The maximal density is determined by the roots of the invariant polynomial. An analogous sharp upper bound is established for a bounded class of finite-gap solutions of the sinh-Gordon equation.

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Otis C. Wright III. 2026-07-03. Maximal Densities of Finite-Gap Solutions of the Sine-Gordon Equation. https://arxiv.org/abs/2607.03555

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