Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917874742853632 |
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| author | Lorenzoni, P. Vitolo, R. |
| author_facet | Lorenzoni, P. Vitolo, R. |
| contents | We study algebraic and projective geometric properties of Hamiltonian trios determined by a constant coefficient second-order operator and two first-order localizable operators of Ferapontov type. We show that first-order operators are determined by Monge metrics, and define a structure of cyclic Frobenius algebra. Examples include the AKNS system, a $2$-component generalization of Camassa-Holm equation and the Kaup--Broer system. In dimension $2$ the trio is completely determined by two conics of rank at least $2$. We provide a partial classification in dimension $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13932 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics Lorenzoni, P. Vitolo, R. Mathematical Physics Primary 37K10 secondary 37K20, 37K25 We study algebraic and projective geometric properties of Hamiltonian trios determined by a constant coefficient second-order operator and two first-order localizable operators of Ferapontov type. We show that first-order operators are determined by Monge metrics, and define a structure of cyclic Frobenius algebra. Examples include the AKNS system, a $2$-component generalization of Camassa-Holm equation and the Kaup--Broer system. In dimension $2$ the trio is completely determined by two conics of rank at least $2$. We provide a partial classification in dimension $4$. |
| title | Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics |
| topic | Mathematical Physics Primary 37K10 secondary 37K20, 37K25 |
| url | https://arxiv.org/abs/2311.13932 |