Dispersionless version of multi-component Pfaff-Toda hierarchy
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909976727912448 |
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| author | Savchenko, A. Zabrodin, A. |
| author_facet | Savchenko, A. Zabrodin, A. |
| contents | We consider the dispersionless limit of the recently introduced multi-component Pfaff-Toda hierarchy. Its dispersionless version is a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the F-function). They are obtained as limiting cases of bilinear equations of the Hirota-Miwa type. The analysis of the Pfaff-Toda hierarchy is substantially simplified by using the observation that the full (not only dispersionless) N-component Pfaff-Toda hierarchy is actually equivalent to the 2N-component DKP hierarchy. In the dispersionless limit, there is an elliptic curve built in the structure of the hierarchy, with the elliptic modular parameter being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization the hierarchy acquires a compact and especially nice form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dispersionless version of multi-component Pfaff-Toda hierarchy Savchenko, A. Zabrodin, A. Exactly Solvable and Integrable Systems Mathematical Physics We consider the dispersionless limit of the recently introduced multi-component Pfaff-Toda hierarchy. Its dispersionless version is a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the F-function). They are obtained as limiting cases of bilinear equations of the Hirota-Miwa type. The analysis of the Pfaff-Toda hierarchy is substantially simplified by using the observation that the full (not only dispersionless) N-component Pfaff-Toda hierarchy is actually equivalent to the 2N-component DKP hierarchy. In the dispersionless limit, there is an elliptic curve built in the structure of the hierarchy, with the elliptic modular parameter being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization the hierarchy acquires a compact and especially nice form. |
| title | Dispersionless version of multi-component Pfaff-Toda hierarchy |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2512.22357 |