聚焦测量修正三格KdV方程超椭圆解的闭实平面曲线

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-05-21 DOI:10.1016/j.geomphys.2025.105540

Shigeki Matsutani

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引用次数: 0

摘要

在复场C上定义的聚焦修正Korteweg-de Vries （MKdV）方程的实部和虚部可得到聚焦测量MKdV （FGMKdV）方程。作为曲率服从聚焦静态MKdV （FSMKdV）方程的欧拉弹性曲线的推广，由于FSMKdV方程是FGMKdV方程的一种特例，我们研究了曲率服从FGMKdV方程的实际平面曲线。本文主要讨论了3属的超椭圆曲线。通过调整一些模参数和初始条件，我们显示了与FGMKdV方程相关的封闭实平面曲线，超出了弹性力学的欧拉数字8。

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

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.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity