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arXiv · 2511.20442

The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach

Anne Boutet de Monvel·Iryna Karpenko·Dmitry Shepelsky·Lech Zielinski
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Abstract

This work addresses the development of the Riemann-Hilbert problem (RHP) formalism (the Fokas method) for the Camassa-Holm equation under periodic boundary conditions. Particularly, we present a representation of the solution to this problem in terms of the solution of the associated Riemann-Hilbert problem, the data for which are determined by the initial data for the problem in terms of the associated spectral functions.

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Anne Boutet de Monvel, Iryna Karpenko, Dmitry Shepelsky, Lech Zielinski. 2025-11-25. The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach. https://arxiv.org/abs/2511.20442

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