Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911359385468928 |
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| author | Nakazono, Nobutaka |
| author_facet | Nakazono, Nobutaka |
| contents | Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an additional parameter admits two types of exact solutions: discrete Painlevé transcendent solutions and periodic solutions described by Painlevé-type ordinary difference equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations Nakazono, Nobutaka Exactly Solvable and Integrable Systems Mathematical Physics Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an additional parameter admits two types of exact solutions: discrete Painlevé transcendent solutions and periodic solutions described by Painlevé-type ordinary difference equations. |
| title | Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2503.06013 |