IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i3p1531-1549.html
   My bibliography  Save this article

Cusped solitons of the Camassa–Holm equation. II. Binary cuspon–soliton interactions

Author

Listed:
  • Parker, A.

Abstract

This paper extends the results of a previous work [Parker A. Cusped solitons of the Camassa–Holm equation. I. Cuspon solitary wave and antipeakon limit. Chaos, Solitons & Fractals 2007;34:730–9]—designated I—in which the solitary cuspon solution of the Camassa–Holm equation and its antipeakon limit were considered. Here, explicit binary cuspon–soliton solutions are obtained in parametric form by exploiting the factorisation procedure that was used in I. The structure and dynamics of these two-wave interactions are investigated and some unanswered questions concerning the waveforms are addressed. In particular, it is shown that, while a cuspon may be ‘swallowed-up’ by a soliton, the converse is never possible regardless of the depth of the cuspon trough. Formulae for the characteristic post-collision phase shifts are obtained and analysed in detail; this permits a reassessment of the previously reported results. Examples of twin-cusped and mixed cuspon–soliton solutions are presented within the different parameter regimes. Coincidentally, we find new two-soliton solutions of the related associated-Camassa–Holm equation. These describe binary interactions of classically smooth elevated solitons and solitary-wave troughs.

Suggested Citation

  • Parker, A., 2009. "Cusped solitons of the Camassa–Holm equation. II. Binary cuspon–soliton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1531-1549.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1531-1549
    DOI: 10.1016/j.chaos.2008.06.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908002853
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.06.023?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. Parker, A., 2007. "Cusped solitons of the Camassa–Holm equation. I. Cuspon solitary wave and antipeakon limit," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 730-739.
    2. Parker, A., 2008. "Wave dynamics for peaked solitons of the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 220-237.
    Full references (including those not matched with items on IDEAS)

    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.

      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:41:y:2009:i:3:p:1531-1549. 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.