Multicomponent DKP hierarchy and its dispersionless limit
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917724891906048 |
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| author | Savchenko, A. Zabrodin, A. |
| author_facet | Savchenko, A. Zabrodin, A. |
| contents | Using the free fermions technique and bosonization rules we introduce the multicomponent DKP hierarchy as a generating bilinear integral equation for the tau-function. A number of bilinear equations of the Hirota-Miwa type are obtained as its corollaries. We also consider the dispersionless version of the hierarchy as a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the $F$-function). We show that there is an elliptic curve built in the structure of the hierarchy, with the elliptic modulus being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization many dispersionless equations of the Hirota-Miwa type become equivalent to a single equation having a nice form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multicomponent DKP hierarchy and its dispersionless limit Savchenko, A. Zabrodin, A. Exactly Solvable and Integrable Systems Mathematical Physics Using the free fermions technique and bosonization rules we introduce the multicomponent DKP hierarchy as a generating bilinear integral equation for the tau-function. A number of bilinear equations of the Hirota-Miwa type are obtained as its corollaries. We also consider the dispersionless version of the hierarchy as a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the $F$-function). We show that there is an elliptic curve built in the structure of the hierarchy, with the elliptic modulus being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization many dispersionless equations of the Hirota-Miwa type become equivalent to a single equation having a nice form. |
| title | Multicomponent DKP hierarchy and its dispersionless limit |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2407.12424 |