从考奇矩阵方法看非谱卡多姆采夫-彼得维亚什维利方程

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

Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI:10.1134/S0040577924100040

A. Y. Tefera, Da-jun Zhang

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引用次数: 0

摘要

为求解非等谱卡多姆采夫-彼得维亚什维利方程和非等谱修正卡多姆采夫-彼得维亚什维利方程开发了考奇矩阵方法。通过西尔维斯特方程（\(\boldsymbol{L})\boldsymbol{M}- \oldsymbol{M}\boldsymbol{K} = \boldsymbol{r}\)，一组标量主函数 \(\{S^{(i,j)}\}) 被定义。我们利用非等谱分散关系推导出标量函数的演化过程。图中给出了一些显式解，并对其进行了动力学分析。

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Nonisospectral Kadomtsev–Petviashvili equations from the Cauchy matrix approach

The Cauchy matrix approach is developed for solving nonisospectral Kadomtsev–Petviashvili equation and the nonisospectral modified Kadomtsev–Petviashvili equation. By means of a Sylvester equation \( \boldsymbol{L} \boldsymbol{M} - \boldsymbol{M} \boldsymbol{K} = \boldsymbol{r} \boldsymbol{s} ^{\mathrm T}\), a set of scalar master functions \(\{S^{(i,j)}\}\) are defined. We derive the evolution of scalar functions using the nonisospectral dispersion relations. Some explicit solutions are illustrated together with the analysis of their dynamics.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.