Bihamiltonian tests for integrable systems associated to rank-1 F-CohFTs

2026/01/19 by Alexandr Buryak, Jianghao Xu, Di Yang · 1 voice · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.AG

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Abstract

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.

Citations

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Discussions

• Alexandr Buryak, Jianghao Xu, Di Yang: Bihamiltonian tests for integrable systems associated to rank-$1$ F-CohFTs https://arxiv.org/abs/2601.13203 https://arxiv.org/pdf/2601.13203 https://arxiv.org/ht [bsky, 0 points, 0 comments]

Related

• Bihamiltonian structure of the DR hierarchy in the semisimple case
• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
• Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT
• On the strong DR/DZ equivalence conjecture
• Finite Group Reduction of the DR/DZ Hierarchies