A LIOUVILLE INTEGRABLE HIERARCHY WITH FOUR POTENTIALS AND ITS BI-HAMILTONIAN STRUCTURE

被引：41
|
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] Mafikeng Campus,Private Bag X2046, ZA-2735 Mmabatho, South Africa
来源：
ROMANIAN REPORTS IN PHYSICS | 2023年 / 75卷 / 03期
关键词：
Matrix spectral problem; Zero curvature equation; Integrable hierar-chy; NLS equations; mKdV equations; SOLITON HIERARCHY; EQUATIONS; TRANSFORMATIONS;
D O I：
10.59277/RomRepPhys.2023.75.115
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We aim to construct a Liouville integrable Hamiltonian hierarchy from a specific matrix spectral problem with four potentials through the zero curvature formulation. The Liouville integrability of the resulting hierarchy is exhibited by a bi-Hamiltonian structure explored by using the trace identity. Illustrative examples of novel four-component coupled Liouville integrable nonlinear Schro center dot dinger equations and modified Korteweg-de Vries equations are presented.
引用
收藏
页数：10
相关论文
共 48 条
  • [1] A combined integrable hierarchy with four potentials and its recursion operator and bi-Hamiltonian structure
    Ma, Wen-Xiu
    INDIAN JOURNAL OF PHYSICS, 2024, : 1063 - 1069
  • [2] AKNS type reduced integrable bi-Hamiltonian hierarchies with four potentials
    Ma, Wen-Xiu
    APPLIED MATHEMATICS LETTERS, 2023, 145
  • [3] A four-component hierarchy of combined integrable equations with bi-Hamiltonian formulations
    Ma, Wen-Xiu
    APPLIED MATHEMATICS LETTERS, 2024, 153
  • [4] A combined Kaup-Newell type integrable hierarchy with four potentials and its bi-Hamiltonian formulation
    Ma, Wen-Xiu
    REVIEWS IN MATHEMATICAL PHYSICS, 2024,
  • [5] FOUR-COMPONENT LIOUVILLE INTEGRABLE MODELS AND THEIR BI-HAMILTONIAN FORMULATIONS
    Yang, Jin-Yun
    Ma, Wen-Xiu
    ROMANIAN JOURNAL OF PHYSICS, 2024, 69 (1-2):
  • [6] Four-component combined integrable equations possessing bi-Hamiltonian formulations
    Ma, Wen-Xiu
    MODERN PHYSICS LETTERS B, 2024, 38 (33):
  • [7] An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation
    Yu, Jing
    Ma, Wen-Xiu
    Han, Jingwei
    Chen, Shouting
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 43 : 151 - 157
  • [8] Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints
    Manukure, Solomon
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 57 : 125 - 135
  • [9] A generalized Dirac soliton hierarchy and its bi-Hamiltonian structure
    Ye, Yujian
    Li, Zhihui
    Li, Chunxia
    Shen, Shoufeng
    Ma, Wen-Xiu
    APPLIED MATHEMATICS LETTERS, 2016, 60 : 67 - 72
  • [10] A six-component integrable hierarchy and its Hamiltonian formulation
    Ma, Wen-Xiu
    MODERN PHYSICS LETTERS B, 2023, 37 (32):
12345