Gibbons-Tsarev type systems and Eventual identities
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911680669155328 |
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| author | Arsie, Alessandro Lorenzoni, Paolo Perletti, Sara van Gemst, Karoline |
| author_facet | Arsie, Alessandro Lorenzoni, Paolo Perletti, Sara van Gemst, Karoline |
| contents | We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple $F$-manifolds cannot exist. The proof is based on the derivation and study of a generalised Gibbons--Tsarev system (gGT system) in the non-semisimple/non-diagonalisable setting. Remarkably, a class of solutions of the gGT system is defined by eventual identities of the underlying regular $F$-manifold structure. Furthermore, we use these vector fields to construct integrable reductions of Pavlov's hydrodynamic chain. In this case, the corresponding solutions are defined for any choice of Jordan block structure of the operator of multiplication by an eventual identity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gibbons-Tsarev type systems and Eventual identities Arsie, Alessandro Lorenzoni, Paolo Perletti, Sara van Gemst, Karoline Mathematical Physics We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple $F$-manifolds cannot exist. The proof is based on the derivation and study of a generalised Gibbons--Tsarev system (gGT system) in the non-semisimple/non-diagonalisable setting. Remarkably, a class of solutions of the gGT system is defined by eventual identities of the underlying regular $F$-manifold structure. Furthermore, we use these vector fields to construct integrable reductions of Pavlov's hydrodynamic chain. In this case, the corresponding solutions are defined for any choice of Jordan block structure of the operator of multiplication by an eventual identity. |
| title | Gibbons-Tsarev type systems and Eventual identities |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.13505 |