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Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation

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  • Zhang, Run-Fa
  • Li, Ming-Chu
  • Albishari, Mohammed
  • Zheng, Fu-Chang
  • Lan, Zhong-Zhou

Abstract

Under investigation in this paper is the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like (CDGKS-like) equation. Based on bilinear neural network method, the generalized lump solution, classical lump solution and the novel analytical solution are constructed by giving some specific activation functions in the single hidden layer neural network model and the “3-2-2” neural network model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained with the help of Maple software. These results fill the blank of the CDGKS-like equation in the existing literature. Via various three-dimensional plots, curve plots, density plots and contour plots, dynamical characteristics of these waves are exhibited. The effective methods used in this paper is helpful to study the nonlinear evolution equations in plasmas, mathematical physics, electromagnetism and fluid dynamics.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002915
    DOI: 10.1016/j.amc.2021.126201
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    References listed on IDEAS

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    1. 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.
    2. Manafian, Jalil & Mohammadi-Ivatloo, Behnam & Abapour, Mehdi, 2019. "Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 13-41.
    3. 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).
    4. Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "Breather-type and multi-wave solutions for (2+1)-dimensional nonlocal Gardner equation," Applied Mathematics and Computation, Elsevier, vol. 390(C).
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    Cited by:

    1. Zhang, Run-Fa & Li, Ming-Chu & Gan, Jian-Yuan & Li, Qing & Lan, Zhong-Zhou, 2022. "Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. 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).

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