IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v191y2025ics0960077924013687.html
   My bibliography  Save this article

Finite dimensional Hamiltonian systems and the algebro-geometry solution of the nonlocal reverse space–time sine-Gordon equation

Author

Listed:
  • Guan, Liang
  • Geng, Xianguo
  • Du, Dianlou
  • Geng, Xue

Abstract

In this paper, we investigate the algebro-geometric solution of the novel integrable nonlocal reverse space–time sine-Gordon equation through the framework of nonlocal finite-dimensional Lie-Poisson Hamiltonian systems, which are generated by the nonlinearization method. The nonlocal reverse space–time sine-Gordon equation is introduced via the Lenard recursion equations. Under suitable constraints, this equation is nonlinearized into two nonlocal finite-dimensional Lie-Poisson Hamiltonian systems. By applying the separated variables, the nonlocal finite-dimensional Lie-Poisson Hamiltonian systems are reformulated as the canonical Hamiltonian systems with the standard symplectic structures. Furthermore, the relationship between the action–angle coordinates and the Jacobi inversion problem is established based on the Hamilton–Jacobi theory. In the end, the algebraic-geometric solution of the nonlocal reverse space–time sine-Gordon equation is obtained using the Riemann-Jacobi inversion.

Suggested Citation

  • Guan, Liang & Geng, Xianguo & Du, Dianlou & Geng, Xue, 2025. "Finite dimensional Hamiltonian systems and the algebro-geometry solution of the nonlocal reverse space–time sine-Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013687
    DOI: 10.1016/j.chaos.2024.115816
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924013687
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115816?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:chsofr:v:191:y:2025:i:c:s0960077924013687. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.