IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2020y2020i1n9260986.html

Rational Solutions and Their Interaction Solutions of the (3 + 1)‐Dimensional Jimbo‐Miwa Equation

Author

Listed:
  • Xiaomin Wang
  • Sudao Bilige
  • Jing Pang

Abstract

In this paper, we gave a form of rational solution and their interaction solution to a nonlinear evolution equation. The rational solution contained lump solution, general lump solution, high‐order lump solution, lump‐type solution, etc. Their interaction solution contained the classical interaction solution, such as the lump‐kink solution and the lump‐soliton solution. As the example, by using the generalized bilinear method and symbolic computation Maple, we obtained abundant high‐order lump‐type solutions and their interaction solutions between lumps and other function solutions under certain constraints of the (3 + 1)‐dimensional Jimbo‐Miwa equation. Via three‐dimensional plots, contour plots and density plots with the help of Maple, the physical characteristics and structures of these waves are described very well. These solutions have greatly enriched the exact solutions of the (3 + 1)‐dimensional Jimbo‐Miwa equation on the existing literature.

Suggested Citation

  • Xiaomin Wang & Sudao Bilige & Jing Pang, 2020. "Rational Solutions and Their Interaction Solutions of the (3 + 1)‐Dimensional Jimbo‐Miwa Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:9260986
    DOI: 10.1155/2020/9260986
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2020/9260986
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/9260986?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. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    2. Wang, Mingliang & Li, Xiangzheng, 2005. "Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1257-1268.
    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. Hasibun Naher & Farah Aini Abdullah, 2012. "The Improved (G’/G)‐Expansion Method for the (2+1)‐Dimensional Modified Zakharov‐Kuznetsov Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Alvaro H. Salas, 2012. "Solving Nonlinear Partial Differential Equations by the sn‐ns Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Lijun Zhang & C. M. Khalique, 2014. "Traveling Wave Solutions and Infinite‐Dimensional Linear Spaces of Multiwave Solutions to Jimbo‐Miwa Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Xie, Xiao-Ran & Zhang, Run-Fa, 2025. "Neural network-based symbolic calculation approach for solving the Korteweg–de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    5. Xiuqing Yu & Fengsheng Xu & Lihua Zhang, 2013. "Abundant Exact Solition‐Like Solutions to the Generalized Bretherton Equation with Arbitrary Constants," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    7. Qing Meng & Bin He, 2016. "Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    8. Sheng, Zhang, 2006. "The periodic wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1213-1220.
    9. Kumar, Sachin & Kumar, Amit, 2022. "Dynamical behaviors and abundant optical soliton solutions of the cold bosonic atoms in a zig-zag optical lattice model using two integral schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 254-274.
    10. Aljohani, A.F. & Alqurashi, Bader Mutair & Kara, A.H., 2021. "Solitons, travelling waves, invariance, conservation laws and ‘approximate’ conservation of the extended Jimbo-Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. Bo Xu & Sheng Zhang, 2022. "Analytical Method for Generalized Nonlinear Schrödinger Equation with Time-Varying Coefficients: Lax Representation, Riemann-Hilbert Problem Solutions," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    12. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    13. Ullah, Mohammad Safi & Baleanu, Dumitru & Ali, M. Zulfikar & Harun-Or-Roshid,, 2023. "Novel dynamics of the Zoomeron model via different analytical methods," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    14. Islam, Md. Ekramul & Mannaf, Md. Abde & Khan, Kamruzzaman & Akbar, M. Ali, 2024. "Soliton’s behavior and stability analysis to a model in mathematical physics," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    15. Khaled A. Gepreel, 2020. "Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics," Mathematics, MDPI, vol. 8(12), pages 1-14, December.
    16. Zayed, Elsayed M.E. & Ahmed, Manar S. & Arnous, Ahmed H. & Yıldırım, Yakup, 2025. "Novel soliton solutions of the (3+1)-dimensional stochastic nonlinear Schrödinger equation in birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    17. Arzu Akbulut & Melike Kaplan & Rubayyi T. Alqahtani & W. Eltayeb Ahmed, 2023. "On the Dynamics of the Complex Hirota-Dynamical Model," Mathematics, MDPI, vol. 11(23), pages 1-12, December.
    18. Li, Donglong & Dai, Zhengde & Guo, Yanfeng & Zhou, Hongwei, 2009. "Doubly periodic wave solution to two-dimensional diffractive-diffusive Ginzburg–Landau equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2288-2296.
    19. Wang, Deng-Shan & Li, Hongbo, 2008. "Symbolic computation and non-travelling wave solutions of (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 383-390.
    20. Seadawy, Aly R. & Ali, Asghar & Althobaiti, Saad & Sayed, Samy, 2021. "Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models," Chaos, Solitons & Fractals, Elsevier, vol. 146(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:2020:y:2020:i:1:n:9260986. 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.