IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v291y2001i1p287-298.html
   My bibliography  Save this article

Solving the KdV hierarchy with self-consistent sources by inverse scattering method

Author

Listed:
  • Lin, Runliang
  • Zeng, Yunbo
  • Ma, Wen-Xiu

Abstract

The evolution of the eigenfunctions in the Lax representation of the KdV hierarchy with self-consistent sources possesses singularity. By proposing a method to treat the singularity to determine the evolution of scattering data, the KdV hierarchy with self-consistent sources is integrated by the inverse scattering method. The soliton solutions of these equations are obtained. It is shown that the insertion of a source may cause the variation of the speed of soliton. This approach can be applied to other (1+1)-dimensional soliton hierarchies.

Suggested Citation

  • Lin, Runliang & Zeng, Yunbo & Ma, Wen-Xiu, 2001. "Solving the KdV hierarchy with self-consistent sources by inverse scattering method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 287-298.
    • Handle: RePEc:eee:phsmap:v:291:y:2001:i:1:p:287-298
    DOI: 10.1016/S0378-4371(00)00519-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100005197
    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(00)00519-7?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.

    References listed on IDEAS

    as
    1. Zeng, Yunbo, 1998. "Constructing hierarchy of sinh-Gordon-type equations from soliton hierarchy with self-consistent source," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 259(3), pages 278-290.
    2. Zeng, Yunbo, 1999. "Bi-hamiltonian structure of JM hierarchy with self-consistent sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(3), pages 405-419.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Babadjanova, Aygul & Kriecherbauer, Thomas & Urazboev, Gayrat, 2020. "The periodic solutions of the discrete modified KdV equation with a self-consistent source," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    2. Wang, Hong-Yan, 2009. "Commutativity of source generation procedure and Bäcklund transformation: A BKP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 779-785.
    3. Xiao, Ting & Zeng, Yunbo, 2005. "A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 38-60.
    4. Gegenhasi, & Hu, Xing-Biao, 2007. "Integrability of a differential-difference KP equation with self-consistent sources," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 145-158.
    5. Li, Qi & Chen, Deng-yuan & Zhang, Jian-bing & Chen, Shou-ting, 2012. "Solving the non-isospectral Ablowitz–Ladik hierarchy via the inverse scattering transform and reductions," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1479-1485.
    6. Bondarenko, N. & Freiling, G. & Urazboev, G., 2013. "Integration of the matrix KdV equation with self-consistent source," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 21-27.

    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.

      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:291:y:2001:i:1:p:287-298. 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: 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.