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.

引用

页码：370 / 387

页数：18

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