IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v45y2012i6p846-852.html
   My bibliography  Save this article

The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method

Author

Listed:
  • Vakhnenko, V.O.
  • Parkes, E.J.

Abstract

A procedure for finding the solutions of the Vakhnenko–Parkes equation by means of the inverse scattering method is described. Both the bound state spectrum and the continuous spectrum are considered in the associated eigenvalue problem. The suggested special form of the singularity function gives rise to periodic solutions. The interaction of a soliton with a one-mode periodic wave is studied.

Suggested Citation

  • Vakhnenko, V.O. & Parkes, E.J., 2012. "The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 846-852.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:846-852
    DOI: 10.1016/j.chaos.2012.02.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077912000707
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2012.02.019?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. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
    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. Vakhnenko, V.O. & Parkes, E.J., 2016. "The inverse problem for some special spectral data," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 116-124.

    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. Akbar, Yasir & Afsar, Haleem & Abbas, Shahzad & Javed, Muhammad Waqas & Ullah, Najib, 2021. "Dromions for the coupled Maccari’s system in fluid mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Hussain, Akhtar & Kara, A.H. & Zaman, F.D., 2023. "An invariance analysis of the Vakhnenko–Parkes Equation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Navickas, Z. & Ragulskis, M. & Telksnys, T., 2016. "Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 333-338.

    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:45:y:2012:i:6:p:846-852. 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: 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.