The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912728962039808 |
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| author | de Monvel, Anne Boutet Karpenko, Iryna Shepelsky, Dmitry Zielinski, Lech |
| author_facet | de Monvel, Anne Boutet Karpenko, Iryna Shepelsky, Dmitry Zielinski, Lech |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach de Monvel, Anne Boutet Karpenko, Iryna Shepelsky, Dmitry Zielinski, Lech Analysis of PDEs Exactly Solvable and Integrable Systems 35Q55, 35Q15, 37K15 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. |
| title | The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach |
| topic | Analysis of PDEs Exactly Solvable and Integrable Systems 35Q55, 35Q15, 37K15 |
| url | https://arxiv.org/abs/2511.20442 |