IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v221y2024icp489-502.html
   My bibliography  Save this article

Higher-order hybrid rogue wave and breather interaction dynamics for the AB system in two-layer fluids

Author

Listed:
  • Ma, Yu-Lan
  • Li, Bang-Qing

Abstract

Rogue waves and breathers emerge as significant solitons, result from ubiquitous nonlinear effects of dynamics in the natural world, science and engineering. In this paper, we study the AB system, a model derived from a two-layer fluid that is widely used to investigate nonlinear fluid dynamics. We use the Darboux transformation to construct analytical solutions for higher-order hybrid rogue waves and breathers, which are expressed by symmetric algebraic matrices. We use these solutions and the spectrum parameters to explore the complex interaction dynamics of the hybrid rogue waves and breathers. We find that the interactions cause significant changes in the phases and shapes. Moreover, we discover an interesting phenomenon: the collisions between the rogue waves and breathers are semi-elastic, meaning that only the phases of the rogue waves change, while the speeds, shapes and phases of the breathers remain the same, before and after the collisions. This study provides new insights into the dynamics of the AB system, and helps us understand nonlinear phenomena in various two-layer fluid systems.

Suggested Citation

  • Ma, Yu-Lan & Li, Bang-Qing, 2024. "Higher-order hybrid rogue wave and breather interaction dynamics for the AB system in two-layer fluids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 489-502.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:489-502
    DOI: 10.1016/j.matcom.2024.03.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542400096X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.03.017?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. Ma, Yu-Lan & Li, Bang-Qing, 2022. "Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Li, Bang-Qing & Ma, Yu-Lan, 2020. "Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Wu, Jianping, 2022. "N-soliton, M-breather and hybrid solutions of a time-dependent Kadomtsev–Petviashvili equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 89-96.
    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.
    1. Suganya, S. & Srividya, B. & Prabhu, A., 2024. "Existence of localized modes in a frustrated ferromagnetic spin chain with added biquadratic interaction," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Cui, Xiao-Qi & Wen, Xiao-Yong & Li, Zai-Dong, 2024. "Magnetization reversal phenomenon of higher-order lump and mixed interaction structures on periodic background in the (2+1)-dimensional Heisenberg ferromagnet spin equation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Mahmoud A. E. Abdelrahman & Emad K. El-Shewy & Y. Omar & N. F. Abdo, 2023. "Modulations of Collapsing Stochastic Modified NLSE Structures," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    4. Ustinov, N.V., 2024. "New type of rogue waves," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    5. Lou, Yu & Zhang, Yi & Ye, Rusuo & Li, Miao, 2021. "Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    6. Qi, Linming & Liu, Lu & Zhao, Weiliang, 2024. "Mixed localized waves in the coupled nonlinear Schrödinger equation with higher-order effects," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    7. Ma, Yu-Lan & Wazwaz, Abdul-Majid & Li, Bang-Qing, 2021. "A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 505-519.
    8. Amira F. Daghistani & Ahmed M. T. Abd El-Bar & Ahmed M. Gemeay & Mahmoud A. E. Abdelrahman & Samia Z. Hassan, 2023. "A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    9. Zhang, Xi & Wang, Yu-Feng & Yang, Sheng-Xiong, 2024. "Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    10. Li, Bang-Qing & Ma, Yu-Lan, 2022. "Interaction properties between rogue wave and breathers to the manakov system arising from stationary self-focusing electromagnetic systems," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    11. Liu, Yaqing & Peng, Linyu, 2023. "Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system," Chaos, Solitons & Fractals, Elsevier, vol. 171(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:matcom:v:221:y:2024:i:c:p:489-502. 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/mathematics-and-computers-in-simulation/ .

    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.