English

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

Analysis of PDEs 2025-11-26 v1 Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.2511.20442,
  title  = {The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach},
  author = {Anne Boutet de Monvel and Iryna Karpenko and Dmitry Shepelsky and Lech Zielinski},
  journal= {arXiv preprint arXiv:2511.20442},
  year   = {2025}
}

Comments

41 pages, 4 figures