IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v233y1996i1p331-354.html
   My bibliography  Save this article

A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization

Author

Listed:
  • Ma, W.X.
  • Fuchssteiner, B.
  • Oevel, W.

Abstract

A 3 × 3 matrix spectral problem for AKNS soliton hierarchy is introduced and the corresponding Bargmann symmetry constraint involving Lax pairs and adjoint Lax pairs is discussed. An explicit new Poisson algebra is proposed and thus the Liouville integrability is established for the nonlinearized spatial system ind a hierarchy of nonlinearized temporal systems under the control of the nonlinearized spatial system. The obtained nonlinearized Lax systems, in which the nonlinearized spatial system is intimately related to stationary AKNS flows, lead to a sort of new involutive solutions to each AKNS soliton equation. Therefore, the binary nonlinearization theory is successfully extended to a case of 3 × 3 matrix spectral problem for AKNS hierarchy.

Suggested Citation

  • Ma, W.X. & Fuchssteiner, B. & Oevel, W., 1996. "A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 233(1), pages 331-354.
  • Handle: RePEc:eee:phsmap:v:233:y:1996:i:1:p:331-354
    DOI: 10.1016/S0378-4371(96)00225-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437196002257
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/S0378-4371(96)00225-7?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. Cao, Jianli & Shi, Wei, 2013. "A new integrable generalized Neumann system related to soliton hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 13-17.
    2. Zeng, Yunbo & Ma, Wen-Xiu, 1999. "The construction of canonical separated variables for binary constrained AKNS flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(3), pages 505-515.

    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:phsmap:v:233:y:1996:i:1:p:331-354. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.