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Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation

Author

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  • Manafian, Jalil
  • Mohammadi-Ivatloo, Behnam
  • Abapour, Mehdi

Abstract

In this article, we use the Hirota bilinear method. With the help of the symbolic calculation and applying the used method, we solve the (2+1)-dimensional Breaking Soliton (BS) equation. We obtain some interaction between lump soliton and solitary wave, the interaction between lump soliton and periodic wave, breather-type periodic soliton, periodic kink-wave, kink-soliton wave, and solitary wave solutions. All solutions have been verified back into its corresponding equation with the aid of Maple package program. The graphical representation of the solution is given by Maple and physically interpreted. The obtained results are useful in gaining the understanding of the various nonlinear scenarios in fluid dynamics and also the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering sciences.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:13-41
    DOI: 10.1016/j.amc.2019.03.016
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    References listed on IDEAS

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    1. Zhang, Wei-Guo & Zhao, Yan-Nan & Chen, Ai-Hua, 2015. "The elastic-fusion-coupled interaction for the Boussinesq equation and new soliton solutions of the KP equation," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 251-257.
    2. Zhang, Yi & Sun, YanBo & Xiang, Wen, 2015. "The rogue waves of the KP equation with self-consistent sources," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 204-213.
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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. 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).
    3. Abdulghani R. Alharbi, 2023. "New Numerical and Analytical Solutions for Nonlinear Evolution Equations Using Updated Mathematical Methods," Mathematics, MDPI, vol. 11(22), pages 1-22, November.

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