与非局部 mKdV 方程相关的非局部有限维可积分系统

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

Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI:10.1134/S0040577924030024

Xue Wang, Dianlou Du, Hui Wang

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引用次数: 0

摘要

摘要我们提出了非局部 mKdV（NmKdV）方程的层次结构。基于约束条件，我们得到了Lie-Poisson结构的非局部有限维可积分系统。通过坐标变换，非局部的列-泊松哈密顿系统被还原为标准交映结构中的非局部典型哈密顿系统。此外，利用非局部有限维可积分系统，我们给出了 NmKdV 方程和广义非局部非线性薛定谔方程（NNLS）的参数解。根据汉密尔顿-雅可比理论，我们得到了与列-泊松汉密尔顿系统相关的作用角型坐标和反演问题。

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A nonlocal finite-dimensional integrable system related to the nonlocal mKdV equation

We propose a hierarchy of the nonlocal mKdV (NmKdV) equation. Based on a constraint, we obtain nonlocal finite-dimensional integrable systems in a Lie–Poisson structure. By a coordinate transformation, the nonlocal Lie–Poisson Hamiltonian systems are reduced to nonlocal canonical Hamiltonian systems in the standard symplectic structure. Moreover, using the nonlocal finite-dimensional integrable systems, we give parametric solutions of the NmKdV equation and the generalized nonlocal nonlinear Schrödinger (NNLS) equation. According to the Hamilton–Jacobi theory, we obtain the action–angle-type coordinates and the inversion problems related to Lie–Poisson Hamiltonian systems.

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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.