2024/10/24 by Shigeki Matsutani, Matsutani, Shigeki · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2410.18496
openalex publication_date 2024/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The real and imaginary parts of the focusing modified Korteweg-de Vries (MKdV) equation defined over the complex field ℂ give rise to the focusing gauged MKdV (FGMKdV) equations. As a generalization of Euler's elastica whose curvature obeys the focusing static MKdV (FSMKdV) equation, we study real plane curves whose curvature obeys the FGMKdV equation since the FSMKdV equation is a special case of the FGMKdV equation. In this paper, we focus on the hyperelliptic curves of genus three. By tuning some moduli parameters and initial conditions, we show closed real plane curves associated with the FGMKdV equation beyond Euler's figure-eight of elastica.