IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1966-d1129356.html
   My bibliography  Save this article

Superposition Formulas and Evolution Behaviors of Multi-Solutions to the (3+1)-Dimensional Generalized Shallow Water Wave-like Equation

Author

Listed:
  • Sudao Bilige

    (Department of Mathemaitcs, Inner Mongolia University of Technology, Hohhote 010051, China)

  • Leilei Cui

    (Department of Mathemaitcs, Inner Mongolia University of Technology, Hohhote 010051, China)

  • Xiaomin Wang

    (Department of Mathemaitcs, Inner Mongolia University of Technology, Hohhote 010051, China)

Abstract

The superposition formulas of multi-solutions to the (3+1)-dimensional generalized shallow water wave-like Equation (GSWWLE) are proposed. There are arbitrary test functions in the superposition formulas of the mixed solutions and the interaction solutions, and we generalized to the sum of any N terms. By freely selecting the test functions and the positive integer N , we have obtained abundant solutions for the GSWWLE. First, we introduced new mixed solutions between two arbitrary functions and the multi-kink solitons, and the abundant mixed solutions were obtained through symbolic computation. Next, we constructed the multi-localized wave solutions which are the superposition of N-even power functions. Finally, the novel interaction solutions between the multi-localized wave solutions and the multi-arbitrary function solutions for the GSWWLE were obtained. The evolution behaviors of the obtained solutions are shown through 3D, contour and density plots. The received results have immensely enriched the exact solutions of the GSWWLE in the available literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1966-:d:1129356
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1966/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1966/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Jingzhu Wu & Xiuzhi Xing & Xianguo Geng, 2015. "Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-9, September.
    3. Yuefeng Zhou & Chuanjian Wang & Xiaoxue Zhang, 2020. "Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    4. Xiaomin Wang & Sudao Bilige & Jing Pang, 2020. "Rational Solutions and Their Interaction Solutions of the ( )- Dimensional Jimbo-Miwa Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-18, April.
    5. Hong-Qian Sun & Zuo-Nong Zhu, 2023. "Darboux Transformation and Soliton Solution of the Nonlocal Generalized Sasa–Satsuma Equation," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    6. 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. Ruijuan Li & Onur Alp İlhan & Jalil Manafian & Khaled H. Mahmoud & Mostafa Abotaleb & Ammar Kadi, 2022. "A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions," Mathematics, MDPI, vol. 10(17), pages 1-17, August.
    2. 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).
    3. 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).
    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. Yu, Weitian & Liu, Wenjun & Zhang, Hongxin, 2022. "Soliton molecules in the kink, antikink and oscillatory background," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. 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.
    7. 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).
    8. 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).
    9. Acharya, S.P. & Janaki, M.S., 2022. "Nonlinear dynamical modelling of high frequency electrostatic drift waves using fluid theoretical approach in magnetized plasma," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    10. 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).
    11. Zhang, Run-Fa & Li, Ming-Chu & Albishari, Mohammed & Zheng, Fu-Chang & Lan, Zhong-Zhou, 2021. "Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    12. 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).

    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:gam:jmathe:v:11:y:2023:i:8:p:1966-:d:1129356. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.