Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus $g$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914274105884672 |
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| author | Matsutani, Shigeki |
| author_facet | Matsutani, Shigeki |
| contents | The real part of the focusing modified Korteweg-de Vries (MKdV) equation defined over the complex field $\mathbb{C}$ is reduced to the focusing gauged MKdV (FGMKdV) equation. In this paper, we construct the real hyperelliptic solutions of FGMKdV equation in terms of data of the hyperelliptic curves of genus $g$ and demonstrate the closed hyperelliptic plane curves of genus $g=5$ whose curvature obeys the FGMKdV equation by extending the previous results of genus three (Matsutani, {\it{J. Geom. Phys}} {\bf{215}} (2025) 105540). These are a generalization of Euler's elasticae. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus $g$ Matsutani, Shigeki Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry The real part of the focusing modified Korteweg-de Vries (MKdV) equation defined over the complex field $\mathbb{C}$ is reduced to the focusing gauged MKdV (FGMKdV) equation. In this paper, we construct the real hyperelliptic solutions of FGMKdV equation in terms of data of the hyperelliptic curves of genus $g$ and demonstrate the closed hyperelliptic plane curves of genus $g=5$ whose curvature obeys the FGMKdV equation by extending the previous results of genus three (Matsutani, {\it{J. Geom. Phys}} {\bf{215}} (2025) 105540). These are a generalization of Euler's elasticae. |
| title | Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus $g$ |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2504.18285 |