IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923007713.html
   My bibliography  Save this article

Investigating overtaking collisions of solitary waves in the Schamel equation

Author

Listed:
  • Flamarion, Marcelo V.
  • Pelinovsky, Efim
  • Didenkulova, Ekaterina

Abstract

This article presents a numerical investigation of overtaking collisions between two solitary waves in the context of the Schamel equation. Our study reveals different regimes characterized by the behavior of the wave interactions. In certain regimes, the collisions maintain two well-separated crests consistently over time, while in other regimes, the number of local maxima undergoes variations following the patterns of 2→1→2→1→2 or 2→1→2. These findings demonstrate that the geometric Lax-categorization observed in the Korteweg–de Vries equation (KdV) for two-soliton collisions remains applicable to the Schamel equation. However, in contrast to the KdV, we demonstrate that an algebraic Lax-categorization based on the ratio of the initial solitary wave amplitudes is not feasible for the Schamel equation. Additionally, we show that the statistical moments for two-solitary wave collisions are qualitatively similar to the KdV equation and the phase shifts after soliton interactions are close to ones in integrable KdV and modified KdV models.

Suggested Citation

  • Flamarion, Marcelo V. & Pelinovsky, Efim & Didenkulova, Ekaterina, 2023. "Investigating overtaking collisions of solitary waves in the Schamel equation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007713
    DOI: 10.1016/j.chaos.2023.113870
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923007713
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113870?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. Marcelo V. Flamarion & Efim Pelinovsky, 2022. "Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework," Mathematics, MDPI, vol. 10(23), pages 1-11, December.
    2. Flamarion, Marcelo V. & Pelinovsky, Efim, 2022. "Soliton interactions with an external forcing: The modified Korteweg–de Vries framework," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    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. Flamarion, Marcelo V. & Pelinovsky, Efim & Didenkulova, Ekaterina, 2024. "Non-integrable soliton gas: The Schamel equation framework," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Ekaterina Didenkulova & Efim Pelinovsky & Marcelo V. Flamarion, 2023. "Bipolar Solitary Wave Interactions within the Schamel Equation," Mathematics, MDPI, vol. 11(22), pages 1-11, November.

    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. Flamarion, Marcelo V. & Pelinovsky, Efim, 2023. "Interactions of solitons with an external force field: Exploring the Schamel equation framework," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Marcelo V. Flamarion & Efim Pelinovsky, 2022. "Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework," Mathematics, MDPI, vol. 10(23), pages 1-11, December.

    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:174:y:2023:i:c:s0960077923007713. 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.