A nonlocal finite-dimensional integrable system related to the nonlocal nonlinear Schrodinger equation hierarchy

IF 2.1 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

International Journal of Geometric Methods in Modern Physics Pub Date : 2023-09-27 DOI:10.1142/s0219887824500452

Xue Wang, Dianlou Du

引用次数: 0

Abstract

Based on the Lenard gradient sequence, a hierarchy of the nonlocal nonlinear Schrödinger (NNLS) equations is obtained. Using the Lax representation, the nonlocal finite-dimensional integrable system with Lie–Poisson structure is presented. Then, under coordinate transformation, the nonlocal finite-dimensional integrable system with Lie–Poisson structure can be expressed as the canonical Hamiltonian system of the standard symplectic structures. Moreover, the parametric representation of the NNLS equation and the nonlocal complex modified Korteweg–de Vries (NcmKdV) equation are constructed. Finally, according to the Hamilton–Jacobi theory, the action–angle variables are built and the inversion problem related to the Lie–Poisson Hamiltonian systems is discussed.

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与非局部非线性薛定谔方程相关的非局部有限维可积系统

基于Lenard梯度序列，得到了非局部非线性Schrödinger (NNLS)方程的层次结构。利用Lax表示，给出了具有Lie-Poisson结构的有限维非局部可积系统。然后在坐标变换下，将具有Lie-Poisson结构的非局部有限维可积系统表示为标准辛结构的正则哈密顿系统。此外，构造了NNLS方程和非局部复修正Korteweg-de Vries (NcmKdV)方程的参数表示。最后，根据Hamilton-Jacobi理论，建立了作用角变量，并讨论了Lie-Poisson hamilton系统的反演问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Geometric Methods in Modern Physics 物理-物理：数学物理

CiteScore

3.40

自引率

22.20%

发文量

274

审稿时长

6 months

期刊介绍： This journal publishes short communications, research and review articles devoted to all applications of geometric methods (including commutative and non-commutative Differential Geometry, Riemannian Geometry, Finsler Geometry, Complex Geometry, Lie Groups and Lie Algebras, Bundle Theory, Homology an Cohomology, Algebraic Geometry, Global Analysis, Category Theory, Operator Algebra and Topology) in all fields of Mathematical and Theoretical Physics, including in particular: Classical Mechanics (Lagrangian, Hamiltonian, Poisson formulations); Quantum Mechanics (also semi-classical approximations); Hamiltonian Systems of ODE''s and PDE''s and Integrability; Variational Structures of Physics and Conservation Laws; Thermodynamics of Systems and Continua (also Quantum Thermodynamics and Statistical Physics); General Relativity and other Geometric Theories of Gravitation; geometric models for Particle Physics; Supergravity and Supersymmetric Field Theories; Classical and Quantum Field Theory (also quantization over curved backgrounds); Gauge Theories; Topological Field Theories; Strings, Branes and Extended Objects Theory; Holography; Quantum Gravity, Loop Quantum Gravity and Quantum Cosmology; applications of Quantum Groups; Quantum Computation; Control Theory; Geometry of Chaos.