论聚焦修正 KdV 方程的实超椭圆解

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-09-30 DOI:10.1007/s11040-024-09490-z

Shigeki Matsutani

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引用次数: 0

摘要

我们研究了属三的聚焦修正 KdV（MKdV）方程的实超椭圆解。由于聚焦 MKdV 方程在 \({{\mathbb {C}}\) 上的复超椭圆解与实高规 MKdV 方程相关，我们提出了一种与高规 MKdV 方程的实超椭圆解相关的新构造。当规量场恒定时，它可以被视为聚焦 MKdV 方程的实解，因此我们也从数值上讨论了规量场的行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Real Hyperelliptic Solutions of Focusing Modified KdV Equation

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On Real Hyperelliptic Solutions of Focusing Modified KdV Equation

We study the real hyperelliptic solutions of the focusing modified KdV (MKdV) equation of genus three. Since the complex hyperelliptic solutions of the focusing MKdV equation over \({{\mathbb {C}}}\) are associated with the real gauged MKdV equation, we present a novel construction related to the real hyperelliptic solutions of the gauged MKdV equation. When the gauge field is constant, it can be regarded as the real solution of the focusing MKdV equation, and thus we also discuss the behavior of the gauge field numerically.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.