IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v240y2026icp938-952.html

Dynamical asymptotic analysis to a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation: The superposition formulas of rational solutions and interaction solutions under the bilinear vector method

Author

Listed:
  • Shao, Hangbing
  • Bilige, Sudao

Abstract

We obtain rational solutions and two types of interaction solutions for a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation based on the Hirota bilinear form. Meanwhile, the bilinear vector method is independently proposed. The bilinear vector method combines computer symbol calculation and manual logic deduction, making it easy to acquire the superposition formula. Three types of solutions exhibit different dynamical behaviors, and they can be obtained based on asymptotic analysis. Especially, two types of interaction solutions differ in spatial globality. The stability of the rational wave as well as the collision behavior of the rational wave and stripe waves are both graphically shown.

Suggested Citation

  • Shao, Hangbing & Bilige, Sudao, 2026. "Dynamical asymptotic analysis to a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation: The superposition formulas of rational solutions and interaction solutions under the bilinear vector method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 938-952.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:938-952
    DOI: 10.1016/j.matcom.2025.07.058
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425003325
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.07.058?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Nandy, Sudipta & Barthakur, Abhijit, 2021. "Dark-bright soliton interactions in coupled nonautonomous nonlinear Schrödinger equation with complex potentials," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Djelah, Gabriel & Ndzana, Fabien II & Abdoulkary, Saidou & Mohamadou, Alidou, 2023. "First and second order rogue waves dynamics in a nonlinear electrical transmission line with the next nearest neighbor couplings," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Biswas, Swapan & Ghosh, Uttam & Raut, Santanu, 2023. "Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. 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.
    5. 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. 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.
    2. 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).
    3. Flamarion, Marcelo V. & Pelinovsky, Efim, 2024. "Solitons in dissipative systems subjected to random force within the Benjamin–Ono type equation," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    4. Wang, Shaoming & Sun, Yiqun & Qi, Jianming & Guo, Peng, 2025. "Research on nonlinear electric transmission model based on Hamiltonian structure with numerical accuracy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    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. Mustafa Inc & Rubayyi T. Alqahtani & Ravi P. Agarwal, 2023. "W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line," Mathematics, MDPI, vol. 11(7), pages 1-13, April.
    7. Zhang, Zhihao & Li, Tiantian & Bai, Xiao-Dong & Zhang, Yunbo & Wang, Denglong, 2026. "High-order rogue waves excited from incident momentum modulation in two-component Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    8. Houwe, Alphonse & Abbagari, Souleymanou & Akinyemi, Lanre & Doka, Serge Yamigno & Metwally, Ahmed Sayed M. & Ahmad, Hijaz, 2024. "Bifurcation and chaotic patterns of the solitary waves in nonlinear electrical transmission line lattice," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    9. Wu, Gang-Zhou & Fang, Yin & Wang, Yue-Yue & Wu, Guo-Cheng & Dai, Chao-Qing, 2021. "Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Xu, Shuwei & He, Jingsong, 2025. "Various rational solutions generated from the higher order Kaup–Newell type equation," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    11. 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).
    12. Hu, Xiang & Yin, Zhixiang, 2022. "A study of the pulse propagation with a generalized Kudryashov equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    13. Adel Elmandouh & Aqilah Aljuaidan & Mamdouh Elbrolosy, 2024. "The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation," Mathematics, MDPI, vol. 12(3), pages 1-15, January.
    14. Mandal, Uttam Kumar & Malik, Sandeep & Kumar, Sachin & Zhang, Yi & Das, Amiya, 2024. "Integrability aspects, rational type solutions and invariant solutions of an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    15. Yuan, Rui-rui & Shi, Ying & Zhao, Song-lin & Wang, Wen-zhuo, 2024. "The mKdV equation under the Gaussian white noise and Wiener process: Darboux transformation and stochastic soliton solutions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    16. Cao, Na & Li, XuHai & Yin, XiaoJun, 2025. "The control model of Rossby waves and dynamic characteristics in stratified fluids," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    17. Fang, Yin & Wu, Gang-Zhou & Kudryashov, Nikolay A. & Wang, Yue-Yue & Dai, Chao-Qing, 2022. "Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    18. Ghosh, Uttam & Roy, Subrata & Biswas, Swapan & Raut, Santanu, 2024. "A non-autonomous fractional granular model: Multi-shock, Breather, Periodic, Hybrid solutions and Soliton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    19. Koyandoulou, C. & Njem, J.S.N. & Takembo, C.N. & Fewo, S.I. & Fouda, H.P.E. & Kofane, T.C., 2025. "Localization of energy in two components model of microtubules under viscosity," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).

    More about this item

    Keywords

    ;
    ;
    ;

    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:eee:matcom:v:240:y:2026:i:c:p:938-952. 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.