卡马萨-霍尔姆方程可积分非等谱层次关联的反散射变换

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-07-11 DOI:10.1016/j.geomphys.2024.105276

Hongyi Zhang, Yufeng Zhang

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引用次数: 0

摘要

我们通过引入非谱拉克斯对来启动这一过程，并由此推导出与卡马萨-霍姆方程相关的可积分非谱层次结构。通过反散射变换方法，我们得到了卡马萨-霍姆方程的可积分非等谱层次结构的 N 索利子解的参数表达式。为了得出无参数解的精确表达式，需要进行坐标变换。为了通过 Gel'fand-Levitan-Marchenko 方程精确地求解孤子解，我们还进行了坐标变换。最后，我们给出了 1 孤子解的图形表示，并分析了其动态行为。

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Inverse scattering transform for integrable nonisospectral hierarchy associate with Camassa-Holm equation

We initiate the process by introducing a nonisospectral Lax pair, from which we derive an integrable nonisospectral hierarchy associate with Camassa-Holm equation. Through the inverse scattering transform method, we obtain parameter expressions for the N-soliton solution of the integrable nonisospectral hierarchy associate with Camassa-Holm equation. To derive the precise expression of the solution without the parameters, a coordinate transformation is performed. In order to work out accurately the soliton solution through the Gel'fand-Levitan-Marchenko equation. Finally, we present the graphical representation of the 1-soliton solution and analyze its dynamic behavior.

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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