IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921008341.html
   My bibliography  Save this article

A study on the resonant multi-soliton waves and the soliton molecule of the (3+1)-dimensional Kudryashov–Sinelshchikov equation

Author

Listed:
  • Kuo, Chun-Ku

Abstract

In this paper, a reduced (3+1)-dimensional nonlinear wave equation describing the dynamic of liquid with gas bubble, namely Kudryashov-Sinelshchikov (KS) equation is carefully investigated. After applying the simplified linear superposition principle (LSP) and the velocity resonance (VR) the fact that there has no existence of soliton molecule to KS equation is formally proofed. Simultaneously, two new resonant multi-soliton solutions constructed with distinct physical structures are also generated. Comparing with the existing ones our solutions are much more general. Most of all, their formula forms reveal the influences of the arbitrary coefficients of the bubble-liquid-dispersion, the y-transverse-perturbation and the z-transverse-perturbation to the traveling soliton waves. Finally, the propagations of inelastic interactions of resonant two-soliton waves are shown in Figures 1-6. Particularly, by specifying special values to the resonant multi-soliton solution gives three-bound-soliton waves moving with the same speed and direction which is in the manner similar to the property of soliton molecule, as shown in Figure 6. The extracted results not only show the efficiency of the simplified LSP but also have potential applications to the physical phenomena of soliton molecules and the resonance of multi-soliton waves .

Suggested Citation

  • Kuo, Chun-Ku, 2021. "A study on the resonant multi-soliton waves and the soliton molecule of the (3+1)-dimensional Kudryashov–Sinelshchikov equation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921008341
    DOI: 10.1016/j.chaos.2021.111480
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008341
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111480?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. Shuxin Yang & Zhao Zhang & Biao Li, 2020. "Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-9, January.
    2. Ma, Wen-Xiu, 2021. "N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 270-279.
    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. Xu, Yuanqing & Zheng, Xiaoxiao & Xin, Jie, 2022. "New non-traveling wave solutions for the (2+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Sudao Bilige & Leilei Cui & Xiaomin Wang, 2023. "Superposition Formulas and Evolution Behaviors of Multi-Solutions to the (3+1)-Dimensional Generalized Shallow Water Wave-like Equation," Mathematics, MDPI, vol. 11(8), pages 1-12, April.
    3. Lü, Xing & Chen, Si-Jia, 2023. "N-soliton solutions and associated integrability for a novel (2+1)-dimensional generalized KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Yin, Yu-Hang & Lü, Xing, 2024. "Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Rafiq, Muhammad Hamza & Raza, Nauman & Jhangeer, Adil, 2023. "Dynamic study of bifurcation, chaotic behavior and multi-soliton profiles for the system of shallow water wave equations with their stability," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    6. Yu, Weitian & Luan, Zitong & Zhang, Hongxin & Liu, Wenjun, 2022. "Collisions of three higher order dark double- and single-hump solitons in optical fiber," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Wen-Xiu Ma, 2022. "Riemann–Hilbert Problems and Soliton Solutions of Type ( λ ∗ , − λ ∗ ) Reduced Nonlocal Integrable mKdV Hierarchies," Mathematics, MDPI, vol. 10(6), pages 1-21, March.
    8. Sugati, Taghreed G. & Seadawy, Aly R. & Alharbey, R.A. & Albarakati, W., 2022. "Nonlinear physical complex hirota dynamical system: Construction of chirp free optical dromions and numerical wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 156(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:chsofr:v:152:y:2021:i:c:s0960077921008341. 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.