Bi-Hamiltonian structures of WDVV-type
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917823056445440 |
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| author | Opanasenko, S. Vitolo, R. |
| author_facet | Opanasenko, S. Vitolo, R. |
| contents | We study a class of nonlinear PDEs that admit the same bi-Hamiltonian structure as WDVV equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order Hamiltonian operator in a canonical Doyle--Potemin form, which are compatible. Using various equivalence groups, we classify such equations in two-component and three-component cases. In a four-component case, we add further evidence to the conjecture that there exists only one integrable system of the above type. Finally, we give an example of the six-component system with required bi-Hamiltonian structure. To streamline the symbolic computation we develop an algorithm to find the aforementioned Hamiltonian operators, which includes putting forward a conjecture on the structure of the metric parameterising the first-order Hamiltonian operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bi-Hamiltonian structures of WDVV-type Opanasenko, S. Vitolo, R. Exactly Solvable and Integrable Systems Mathematical Physics 37K10 We study a class of nonlinear PDEs that admit the same bi-Hamiltonian structure as WDVV equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order Hamiltonian operator in a canonical Doyle--Potemin form, which are compatible. Using various equivalence groups, we classify such equations in two-component and three-component cases. In a four-component case, we add further evidence to the conjecture that there exists only one integrable system of the above type. Finally, we give an example of the six-component system with required bi-Hamiltonian structure. To streamline the symbolic computation we develop an algorithm to find the aforementioned Hamiltonian operators, which includes putting forward a conjecture on the structure of the metric parameterising the first-order Hamiltonian operator. |
| title | Bi-Hamiltonian structures of WDVV-type |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 37K10 |
| url | https://arxiv.org/abs/2407.17189 |