Lax pairs for BKM hierarchy
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915695040659456 |
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| author | Konyaev, Andrey Yu. Matveev, Vladimir S. |
| author_facet | Konyaev, Andrey Yu. Matveev, Vladimir S. |
| contents | We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cases of the BKM systems, our construction provides Lax pairs for many integrable hierarchies, including previously studied ones such as Camassa-Holm, Dullin-Gottwald-Holm, cKdV, Ito, and Marvan-Pavlov, as well as new ones. The corresponding pair is related to a Sturm-Liouville operator on the real line whose potential depends rationally on the spectral parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lax pairs for BKM hierarchy Konyaev, Andrey Yu. Matveev, Vladimir S. Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Differential Geometry 37K10, 35B06, 35C07, 35C08 We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cases of the BKM systems, our construction provides Lax pairs for many integrable hierarchies, including previously studied ones such as Camassa-Holm, Dullin-Gottwald-Holm, cKdV, Ito, and Marvan-Pavlov, as well as new ones. The corresponding pair is related to a Sturm-Liouville operator on the real line whose potential depends rationally on the spectral parameter. |
| title | Lax pairs for BKM hierarchy |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Differential Geometry 37K10, 35B06, 35C07, 35C08 |
| url | https://arxiv.org/abs/2512.22064 |