On algebro-geometric solutions to the Gelfand--Dickey hierarchy
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911496411283456 |
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| author | Zhou, Zejun |
| author_facet | Zhou, Zejun |
| contents | In [14] Dubrovin introduced an $A_1$-type infinite ODE system and gave a simple way of constructing algebro-geometric solutions to the KdV hierarchy (cf. also [15,4]). In [34] the infinite ODE system is generalized to $\mathfrak{g}$-type infinite ODE system, where $\mathfrak{g}$ is any simple Lie algebra. In this paper, we give a simple constructinon of algebro-geometric solutions to the Gelfand--Dickey hierarchy based on the $A_n$-type infinite ODE system and Dubrovin's method. As an application, we give a formula for the $N$-point function for the related Riemann $θ$-function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07636 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On algebro-geometric solutions to the Gelfand--Dickey hierarchy Zhou, Zejun Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry In [14] Dubrovin introduced an $A_1$-type infinite ODE system and gave a simple way of constructing algebro-geometric solutions to the KdV hierarchy (cf. also [15,4]). In [34] the infinite ODE system is generalized to $\mathfrak{g}$-type infinite ODE system, where $\mathfrak{g}$ is any simple Lie algebra. In this paper, we give a simple constructinon of algebro-geometric solutions to the Gelfand--Dickey hierarchy based on the $A_n$-type infinite ODE system and Dubrovin's method. As an application, we give a formula for the $N$-point function for the related Riemann $θ$-function. |
| title | On algebro-geometric solutions to the Gelfand--Dickey hierarchy |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2603.07636 |