Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908394344939520 |
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| author | Kimura, Hironobu |
| author_facet | Kimura, Hironobu |
| contents | We construct solutions of the 2-dimensional Toda-Hirota equation (2dTHE) expressed by the solutions of the system of so-called Euler-Poisson-Darboux equations (EPD) in N complex variables. The system of EPD arises naturally from the differential equations which form a main body of the system characterizing the Gelfand hypergeometric function (Gelfand HGF) on the Grassmannian GM$(2,N)$. Using this link and the contiguity relations for the Gelfand HGF, which are constructed from root vectors for the root $ε_i-ε_j$ for $\mathfrak{gl}(N)$, we show that the Gelfand HGF gives solutions of the 2dTHE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Kimura, Hironobu Classical Analysis and ODEs 33C70, 35Q05, 35Q51 We construct solutions of the 2-dimensional Toda-Hirota equation (2dTHE) expressed by the solutions of the system of so-called Euler-Poisson-Darboux equations (EPD) in N complex variables. The system of EPD arises naturally from the differential equations which form a main body of the system characterizing the Gelfand hypergeometric function (Gelfand HGF) on the Grassmannian GM$(2,N)$. Using this link and the contiguity relations for the Gelfand HGF, which are constructed from root vectors for the root $ε_i-ε_j$ for $\mathfrak{gl}(N)$, we show that the Gelfand HGF gives solutions of the 2dTHE. |
| title | Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation |
| topic | Classical Analysis and ODEs 33C70, 35Q05, 35Q51 |
| url | https://arxiv.org/abs/2506.04638 |