IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v23y2005i5p1911-1919.html
   My bibliography  Save this article

A generalized AKNS hierarchy and its bi-Hamiltonian structures

Author

Listed:
  • Xia, Tiecheng
  • You, Fucai
  • Chen, Dengyuan

Abstract

First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator.

Suggested Citation

  • Xia, Tiecheng & You, Fucai & Chen, Dengyuan, 2005. "A generalized AKNS hierarchy and its bi-Hamiltonian structures," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1911-1919.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:5:p:1911-1919
    DOI: 10.1016/j.chaos.2004.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077904004552
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2004.07.004?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. You, Fucai & Xia, Tiecheng, 2009. "Application of a semi-direct sum of Lie algebras to the TD hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2750-2755.

    More about this item

    Statistics

    Access and download statistics

    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:23:y:2005:i:5:p:1911-1919. 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.