IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2021y2021i1n6643512.html

Application of the Multiple Exp‐Function, Cross‐Kink, Periodic‐Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

Author

Listed:
  • Haifa Bin Jebreen
  • Yurilev Chalco-Cano

Abstract

In this article, the exact wave structures are discussed to the Caudrey‐Dodd‐Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic‐kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic‐kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2‐dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics.

Suggested Citation

  • Haifa Bin Jebreen & Yurilev Chalco-Cano, 2021. "Application of the Multiple Exp‐Function, Cross‐Kink, Periodic‐Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6643512
    DOI: 10.1155/2021/6643512
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2021/6643512
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2021/6643512?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
    ---><---

    References listed on IDEAS

    as
    1. 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).
    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. Wu, Xi-Hu & Gao, Yi-Tian, 2025. "Multi-breather asymptotics for a nonlinear Schrödinger equation arising in oceanography, plasma physics, Bose–Einstein condensation and fiber optics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 235(C), pages 85-94.
    2. 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.
    3. Jin, Xin-Wei & Zhao, Yi-Miao & Duan, Liang & Yang, Zhan-Ying & Yang, Wen-Li, 2024. "Voltage manipulation of magnetic rogue waves for controllable electromagnetic interference," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    4. Jin, Xin-Wei & Liu, Yanan & Duan, Liang & Yang, Zhan-Ying & Liao, Zhi-Min & Jing, Guangyin, 2025. "Excitation and positioning of spin rogue waves," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    5. Zhigang Yao & Huayong Xie & Hui Jie, 2021. "Mixed Rational Lump‐Solitary Wave Solutions to an Extended (2+1)‐Dimensional KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    6. 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).
    7. 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.
    8. 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).
    9. 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).
    10. 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).
    11. 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).

    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:wly:jnlamp:v:2021:y:2021:i:1:n:6643512. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    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.