IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v353y2005icp38-60.html
   My bibliography  Save this article

A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources

Author

Listed:
  • Xiao, Ting
  • Zeng, Yunbo

Abstract

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generalized Darboux transformation with arbitrary functions in time t for the mKPESCS which, in contrast with the Darboux transformation for the mKP equation, provides a nonauto-Bäcklund transformation between two mKPESCSs with different degrees. The formula for n-times repeated generalized Darboux transformation is proposed and enables us to find the rational solutions (including the lump solutions), soliton solutions and the solutions of breather type of the mKPESCS.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:38-60
    DOI: 10.1016/j.physa.2005.02.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105001056
    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/j.physa.2005.02.043?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. 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.
    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. 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.
    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.

    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. 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.
    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. 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.
    4. 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.
    5. 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).

    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:353:y:2005:i:c:p:38-60. 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.