Hyperelliptic sigma functions and the Kadomtsev-Petviashvili equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911063008608256 |
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| author | Ayano, Takanori Buchstaber, Victor M. |
| author_facet | Ayano, Takanori Buchstaber, Victor M. |
| contents | In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev-Petviashvili equations KP-I and KP-II are obtained. The long-standing problem of describing the dependence of these solutions on the variation of the coefficients of the defining equation of a hyperelliptic curve, which are integrals of the equations, is solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperelliptic sigma functions and the Kadomtsev-Petviashvili equation Ayano, Takanori Buchstaber, Victor M. Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems 14H42, 14K25, 14H70, 14H81 In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev-Petviashvili equations KP-I and KP-II are obtained. The long-standing problem of describing the dependence of these solutions on the variation of the coefficients of the defining equation of a hyperelliptic curve, which are integrals of the equations, is solved. |
| title | Hyperelliptic sigma functions and the Kadomtsev-Petviashvili equation |
| topic | Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems 14H42, 14K25, 14H70, 14H81 |
| url | https://arxiv.org/abs/2502.19972 |