An extended AKNS eigenvalue problem and its affiliated integrable Hamiltonian hierarchies

被引：2

作者：

Ma, Wen-Xiu ^{[1
,2
,3
,4
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

[3] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

[4] North West Univ, Dept Math Sci, Mat Sci Innovat & Modelling, Mafikeng Campus, ZA-2735 Mmabatho, South Africa

来源：

CHAOS SOLITONS & FRACTALS | 2024年 / 188卷

基金：

中国国家自然科学基金;

关键词：

Matrix eigenvalue problem; Lax pair; Zero curvature equation; Integrable model; Bi-Hamiltonian formulation; NONLINEAR EVOLUTION-EQUATIONS; COUPLINGS;

D O I：

10.1016/j.chaos.2024.115580

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper aims to study an extended 4 x 4 AKNS eigenvalue problem and construct its affiliated integrable hierarchies of bi-Hamiltonian models over the real field. The Lax pair framework serves as the fundamental tool, ensuring integrability through bi-Hamiltonian structures with hereditary recursion operators. We compute illustrative examples of lower-order equations to demonstrate the affiliated integrable hierarchies.

引用

页数：6

共 30 条

[21] Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form
Nakamura Y.
Japan Journal of Industrial and Applied Mathematics, 1997, 14 (2) : 159 - 168
[22] A LIOUVILLE INTEGRABLE HIERARCHY WITH FOUR POTENTIALS AND ITS BI-HAMILTONIAN STRUCTURE
Ma, Wen-Xiu
ROMANIAN REPORTS IN PHYSICS, 2023, 75 (03)
[23] A combined Kaup-Newell type integrable hierarchy with four potentials and its bi-Hamiltonian formulation
Ma, Wen-Xiu
REVIEWS IN MATHEMATICAL PHYSICS, 2024,
[24] A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem
Ma, Wen-Xiu
MATHEMATICS, 2024, 12 (06)
[25] A Bi-Hamiltonian Lattice System of Rational Type and Its Discrete Integrable Couplings
YANG Hong-Xiang~1 CAO Wei-Li~2 HOU Ying-Kun~1 ZHU Xiang-Cai~1Department of Information Science and Technology
CommunicationsinTheoreticalPhysics, 2008, 50 (09) : 593 - 597
[26] Bi-Hamiltonian lattice system of rational type and its discrete integrable couplings
Yang Hong-Xiang
Cao Wei-Li
Hou Ying-Kun
Zhu Xiang-Cai
COMMUNICATIONS IN THEORETICAL PHYSICS, 2008, 50 (03) : 593 - 597
[27] A generalized super AKNS hierarchy associated with Lie -superalgebra sl(2|1) and its super bi-Hamiltonian structure
Han, Jingwei
Yu, Jing
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 44 : 258 - 265
[28] A subalgebra of Lie algebra A2 and its associated two types of loop algebras, as well as Hamiltonian structures of integrable hierarchy
Dong Huan-he
JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (05)
[29] Two types of Lie super-algebra for the super-integrable Tu-hierarchy and its super-Hamiltonian structure
Wang Xin-zeng
Liu Xi-kui
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (08) : 2044 - 2049
[30] Four-component integrable hierarchies of Hamiltonian equations with (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m+n+2$$\end{document})th-order Lax pairs
Wen-Xiu Ma
Theoretical and Mathematical Physics, 2023, 216 (2) : 1180 - 1188

← 1 2 3 →