Bihamiltonian tests for integrable systems associated to rank-$1$ F-CohFTs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915739322023936 |
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| author | Buryak, Alexandr Xu, Jianghao Yang, Di |
| author_facet | Buryak, Alexandr Xu, Jianghao Yang, Di |
| contents | Double ramification (DR) hierarchies associated to rank-$1$ F-CohFTs are important integrable perturbations of the Riemann--Hopf hierarchy. In this paper, we perform bihamiltonian tests for these DR hierarchies, and conjecture that the ones that are bihamiltonian form a $2$-parameter family. Remarkably, our computations suggest that there is a $1$-parameter subfamily of the rank-$1$ F-CohFTs, where the corresponding DR hierarchy is conjecturally Miura equivalent to the Camassa--Holm hierarchy. We also prove a conjecture regarding bihamiltonian Hodge hierarchies. Finally, we systematically study Miura invariants, and for another $1$-parameter subfamily propose a conjectural relation to the Degasperis--Procesi hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13203 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bihamiltonian tests for integrable systems associated to rank-$1$ F-CohFTs Buryak, Alexandr Xu, Jianghao Yang, Di Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry Double ramification (DR) hierarchies associated to rank-$1$ F-CohFTs are important integrable perturbations of the Riemann--Hopf hierarchy. In this paper, we perform bihamiltonian tests for these DR hierarchies, and conjecture that the ones that are bihamiltonian form a $2$-parameter family. Remarkably, our computations suggest that there is a $1$-parameter subfamily of the rank-$1$ F-CohFTs, where the corresponding DR hierarchy is conjecturally Miura equivalent to the Camassa--Holm hierarchy. We also prove a conjecture regarding bihamiltonian Hodge hierarchies. Finally, we systematically study Miura invariants, and for another $1$-parameter subfamily propose a conjectural relation to the Degasperis--Procesi hierarchy. |
| title | Bihamiltonian tests for integrable systems associated to rank-$1$ F-CohFTs |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2601.13203 |