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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.16233 |
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| _version_ | 1866914483836813312 |
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| author | Quaschner, Manuel Steneker, Wijnand |
| author_facet | Quaschner, Manuel Steneker, Wijnand |
| contents | We show that jets of initial data can be approximated up to arbitrary order by finite-gap solutions for classes of so-called BKM systems of PDEs introduced by Bolsinov--Konyaev--Matveev, which include classical PDEs such as KdV, Kaup--Boussinesq and Camassa--Holm. Finite-gap solutions are obtained via a finite-reduction map, defined algebraically, which sends solutions of a Stäckel system to solutions of the BKM PDE. For the classes containing KdV and Kaup--Boussinesq we obtain full jet-surjectivity via a triangular structure, whereas for the class containing Camassa--Holm we establish jet-surjectivity on an open set of initial data over $\mathbb{R}$ and a Zariski-open (dense) set over $\mathbb{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16233 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jet-Density of Finite-Gap Solutions for Classes of BKM Systems Quaschner, Manuel Steneker, Wijnand Analysis of PDEs Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 37K15, 37K10 We show that jets of initial data can be approximated up to arbitrary order by finite-gap solutions for classes of so-called BKM systems of PDEs introduced by Bolsinov--Konyaev--Matveev, which include classical PDEs such as KdV, Kaup--Boussinesq and Camassa--Holm. Finite-gap solutions are obtained via a finite-reduction map, defined algebraically, which sends solutions of a Stäckel system to solutions of the BKM PDE. For the classes containing KdV and Kaup--Boussinesq we obtain full jet-surjectivity via a triangular structure, whereas for the class containing Camassa--Holm we establish jet-surjectivity on an open set of initial data over $\mathbb{R}$ and a Zariski-open (dense) set over $\mathbb{C}$. |
| title | Jet-Density of Finite-Gap Solutions for Classes of BKM Systems |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 37K15, 37K10 |
| url | https://arxiv.org/abs/2604.16233 |