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Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies

Author

Listed:
  • Shou-Ting Chen

    (School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221008, China)

  • Wen-Xiu Ma

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
    School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa)

Abstract

Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations are worked out.

Suggested Citation

  • Shou-Ting Chen & Wen-Xiu Ma, 2023. "Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies," Mathematics, MDPI, vol. 11(8), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1794-:d:1119418
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    References listed on IDEAS

    as
    1. Xiao-ming Zhu & Jian-bing Zhang & Yao Zhong Zhang, 2022. "The Integrability of a New Fractional Soliton Hierarchy and Its Application," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-14, May.
    2. Yuqin Yao & Shoufeng Shen & Wen-Xiu Ma, 2016. "A Soliton Hierarchy Associated with a Spectral Problem of 2nd Degree in a Spectral Parameter and Its Bi-Hamiltonian Structure," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-6, March.
    3. Xia, Tiecheng & Yu, Fajun & Zhang, Yi, 2004. "The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 238-246.
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