IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v125y1984i2p344-380.html
   My bibliography  Save this article

Linear integral equations and nonlinear difference-difference equations

Author

Listed:
  • Quispel, G.R.W.
  • Nijhoff, F.W.
  • Capel, H.W.
  • Van Der Linden, J.

Abstract

In this paper we present a systematic method to obtain various integrable nonlinear difference-difference equations and the associated linear integral equations from which their solutions can be inferred. It is argued that these difference-difference equations can be regarded as arising from Bianchi identities expressing the commutativity of Bäcklund transformations. Applying an appropriate continuum limit we first obtain integrable nonlinear differential-difference equations together with the associated linear integral equations and after a second continuum limit we can obtain the corresponding integrable nonlinear partial differential equations and their linear integral equations. As special cases we treat the difference-difference versions and the differential-difference versions of the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the nonlinear Schrödinger equation, the isotropic classical Heisenberg spin chain, and the complex and real sine-Gordon equation.

Suggested Citation

  • Quispel, G.R.W. & Nijhoff, F.W. & Capel, H.W. & Van Der Linden, J., 1984. "Linear integral equations and nonlinear difference-difference equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 344-380.
    • Handle: RePEc:eee:phsmap:v:125:y:1984:i:2:p:344-380
    DOI: 10.1016/0378-4371(84)90059-1
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437184900591
    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/10.1016/0378-4371(84)90059-1?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. Moerniati Samsono & F. Tumiwa & M.M. Sangian & Soedrajat Djiwandono & Moh. Sadli & Sumitro DJofohadikusumo, 1981. "Tinjauan Triwulan Perekonomian Indonesia," Economics and Finance in Indonesia, Faculty of Economics and Business, University of Indonesia, vol. 29, pages 107-148, Juni.
    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. Sahadevan, R. & Capel, H.W., 2003. "Complete integrability and singularity confinement of nonautonomous modified Korteweg–de Vries and sine Gordon mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 373-390.
    2. Capel, H.W. & Sahadevan, R., 2001. "A new family of four-dimensional symplectic and integrable mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 86-106.
    3. Haggar, F.A. & Byrnes, G.B. & Quispel, G.R.W. & Capel, H.W., 1996. "k-integrals and k-Lie symmetries in discrete dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 233(1), pages 379-394.

    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. Perk, J.H.H. & Capel, H.W. & Quispel, G.R.W. & Nijhoff, F.W., 1984. "Finite-temperature correlations for the Ising chain in a transverse field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(1), pages 1-49.

    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:phsmap:v:125:y:1984:i:2:p:344-380. 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.