Integrable geometric evolution equations through a deformed Heisenberg spin equation

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-05-19 DOI:10.1016/j.geomphys.2025.105534

Dae Won Yoon , Zühal Küçükarslan Yüzbaşı

引用次数: 0

Abstract

Using the geometrical equivalence methods, we showed a deformed Heisenberg spin chain equation is geometrically equivalent to a generalized nonlinear Schrödinger equation. After that, we demonstrate in Euclidean 3-space that assigning spin vectors to the tangent, normal, and binormal vectors of the three distinct moving space curves, respectively, results in the creation of three distinct surfaces. Then we find the Gauss and the mean curvatures of these surfaces, respectively.

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通过变形海森堡自旋方程可积几何演化方程

利用几何等价方法，证明了变形海森堡自旋链方程与广义非线性Schrödinger方程的几何等价。之后，我们在欧几里得三维空间中证明，分别将自旋向量分配给三个不同的移动空间曲线的切线、法线和二法线向量，会产生三个不同的表面。然后分别求出这些曲面的高斯曲率和平均曲率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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