Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI:10.1134/s0040577924050039

Haifeng Wang, Yufeng Zhang

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Abstract

We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a \(Z_N^\varepsilon\) nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity.

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生成与一类新的高维列向量环代数相关的高维等谱-非等谱可积分层次结构

摘要我们构建了一类新的高维列向量环代数。在此基础上，我们提出了一种生成高维等谱-非等谱可积分层次结构的方法。作为一种应用，我们推导了一种广义的非等谱可积分薛定谔层次结构，它可以简化为著名的导数非线性薛定谔方程。通过使用高维柱向量环代数，我们得到了扩展的等谱-非等谱可积分薛定谔层次，它可以还原到许多经典方程和新方程，如扩展的非等谱导数非线性薛定谔系统、热方程和福克-普朗克方程，在随机动力学系统中有着广泛的应用。此外，我们还推导出了（Z_N^\varepsilon\）非等谱可积分薛定谔层次结构，这意味着耦合结果可以扩展到任意数量的分量。此外，我们还利用二次型痕量特性讨论了这些层次结构的哈密顿结构。

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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.