多分量离散可积层次及其哈密顿结构

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-22 DOI:10.1007/s11040-025-09523-1

Haifeng Wang, Zhenzhu Fang, Jian Li, Chuanzhong Li

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引用次数: 0

摘要

引入了一类无限维李代数，给出了一种生成多分量离散可积孤子方程组的格式。提出了一个多分量离散二次型恒等式，可用于建立多分量离散可积层次的哈密顿结构。考虑到应用，我们得到了一个耦合的和一个多分量的Volterra晶格层次及其Liouville可积哈密顿结构。

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Multi-component discrete integrable hierarchy and its Hamiltonian structure

We introduce a kind of infinite-dimensional Lie algebra, it follows that a scheme for generating multi-component discrete integrable hierarchy of soliton equations is proposed. A multi-component discrete quadratic-form identity is presented which could be used to establish Hamiltonian structures of multi-component discrete integrable hierarchies. By considering the application, we obtain a coupled and a multi-component Volterra lattice hierarchies and their Liouville integrable Hamiltonian structures.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.