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A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves

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  • Ma, Yu-Lan
  • Wazwaz, Abdul-Majid
  • Li, Bang-Qing

Abstract

In this paper, a new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed. Its integrability is verified by the Painlevé analysis. The bilinear form, multiple-soliton, breather and lump solutions are obtained via using the Hirota bilinear method, a symbolic computation scheme. Furthermore, the abundant dynamical behaviors for these solutions are discovered. It is interesting that there are splitting and fusing phenomena when the lump waves interact. The results can well simulate complex waves and their interaction dynamics in fluids.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:505-519
    DOI: 10.1016/j.matcom.2021.03.012
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    References listed on IDEAS

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    1. Guan, Xue & Liu, Wenjun & Zhou, Qin & Biswas, Anjan, 2020. "Some lump solutions for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    2. Na Xiong & Wen-Tao Li & Biao Li, 2020. "Weakly Coupled B-Type Kadomtsev-Petviashvili Equation: Lump and Rational Solutions," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-8, September.
    3. 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).
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    Cited by:

    1. Sivenathi Oscar Mbusi & Ben Muatjetjeja & Abdullahi Rashid Adem, 2021. "Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation," Mathematics, MDPI, vol. 9(22), pages 1-10, November.
    2. Alsufi, Nizar Abdallah & Fatima, Nahid & Noor, Adeeb & Gorji, M.R. & Alam, Mohammad Mahtab, 2023. "Lumps and interactions, fission and fusion phenomena in multi solitons of extended Shallow Water Wave Equation of (2+1)-dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Cao, Na & Yin, XiaoJun & Bai, ShuTing & LiYangXu,, 2023. "Breather wave, lump type and interaction solutions for a high dimensional evolution model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. 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).
    5. Liu, Yaqing & Peng, Linyu, 2023. "Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    6. Li, Lingfei & Zhu, Minting & Zheng, Han & Xie, Yingying, 2023. "Non-compatible partially PT symmetric Davey–Stewartson system: Rational and semi-rational solution with nonzero background," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Ma, Yu-Lan & Li, Bang-Qing, 2022. "Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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