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

被引：3

作者：

Wang, Xue ^{[1
]}

Du, Dianlou ^{[2
]}

机构：

[1] Henan Univ Engn, Coll Sci, Zhengzhou 451191, Henan, Peoples R China

[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2024年 / 21卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nonlocal integrable system; NNLS equation; action-angle variables; Lie-Poisson Hamiltonian systems; INVERSE SCATTERING; SOLITON-SOLUTIONS; RESTRICTED FLOWS; COUPLED KDV; STATIONARY;

D O I：

10.1142/S0219887824500452

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Based on the Lenard gradient sequence, a hierarchy of the nonlocal nonlinear Schrodinger (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 Kortewegde 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.

引用

页数：34

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