IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1794-d1119418.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1794/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1794/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ma, Wen-Xiu & Meng, Jinghan & Zhang, Mengshu, 2016. "Nonlinear bi-integrable couplings with Hamiltonian structures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 166-177.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1794-:d:1119418. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.