从考奇矩阵方法看非谱方程

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-08-01 DOI:10.1016/S0034-4877(24)00055-7

Alemu Yilma Tefera, Shangshuai Li, Da-jun Zhang

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引用次数: 0

摘要

本研究开发了考希矩阵方法，用于构建一些非等谱方程的显式解，包括非等谱 Korteweg-de Vries (KdV) 方程、非等谱修正 KdV 方程和非等谱正弦-戈登方程。通过西尔维斯特方程，定义了一组标量主函数 {S(i,j)}。我们将展示如何引入非等谱分散关系，从而推导出 {S(i,j)} 的演化过程。在验证解决方案时，我们使用了{S(i,j)}的一些同义词。一些明确的单孑子和双孑子解将与其动力学分析一起说明。

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Nonisospectral equations from the Cauchy matrix approach

The Cauchy matrix approach is developed to construct explicit solutions for some nonisospectral equations, including the nonisospectral Korteweg–de Vries (KdV) equation, the nonisospectral modified KdV equation, and the nonisospectral sine-Gordon equation. By means of a Sylvester equation, a set of scalar master functions {S^(i,j)} is defined. We show how nonisospectral dispersion relations are introduced such that the evolutions of {S^(i,j)} can be derived. Some identities of {S^(i,j)} are employed in verifying solutions. Some explicit one-soliton and two-soliton solutions are illustrated together with analysis of their dynamics.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.