A NONLOCAL FINITE-DIMENSIONAL INTEGRABLE SYSTEM RELATED TO THE NONLOCAL MKDV EQUATION

被引：0
|
作者：
Wang, Xue [1 ,2 ]
Du, Dianlou [2 ]
Wang, Hui [1 ]
机构：
[1] Henan Univ Engn, Coll Sci, Zhengzhou, Henan, Peoples R China
[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou, Henan, Peoples R China
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2024年 / 218卷 / 03期
基金：
中国国家自然科学基金;
关键词：
nonlocal integrable system; nonlocal mKdV equation; Lie-Poisson Hamiltonian system; action-angle type variables; NONLINEAR SCHRODINGER-EQUATIONS; DE-VRIES EQUATION; SOLITON-SOLUTIONS;
D O I：
10.1134/S0040577924030024
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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 Schrodinger (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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页码：370 / 387
页数：18
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