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arXiv · 2504.18285

Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus $g$

Shigeki Matsutani
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Abstract

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.

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Shigeki Matsutani. 2025-04-25. Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus $g$. https://arxiv.org/abs/2504.18285

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