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Interactions of rogue and solitary wave solutions to the (2 + 1)-D generalized Camassa–Holm–KP equation

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Abstract

This research explores a (2 + 1)-D generalized Camassa–Holm–Kadomtsev–Petviashvili model. We use a probable transformation to build bilinear formulation to the model by Hirota bilinear technique. We derive a single lump waves, multi-soliton solutions to the model from this bilinear form. We present various dynamical properties of the model such as one, two, three and four solitons. The double periodic breather waves, periodic line rogue wave, interaction between bell soliton and double periodic rogue waves, rogue and bell soliton, rogue and two bell solitons, two rogues, rogue and periodic wave, double periodic waves, two pair of rogue waves as well as interaction of double periodic rogue waves in a line are established. Among the results, most of the properties are unexplored in the prior research. Furthermore, with the assistance of Maple software, we put out the trajectory of the obtained solutions for visualizing the achieved dynamical properties.

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The authors sketched the dynamical interactions of solitons and rogue with Maple. So, supported data are included inside this article and not taken from outside sources.

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Acknowledgements

Thanks to editor, reviewers and to Khalifa University, Abu Dhabi, United Arab Emirates, for financial support in this research.

Funding

This research was partially funded by Khalifa University, Abu Dhabi, United Arab Emirates, and Prince Sattam bin Abdulaziz University, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, Khalifa University, Abu Dhabi, United Arab Emirates

    Alrazi Abdeljabbar

  2. Department of Computer Science and Engineering, Uttara University, Dhaka, Bangladesh

    M. Belal Hossen

  3. Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh

    Harun-Or Roshid

  4. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, 11942, Saudi Arabia

    Abdullah Aldurayhim

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  1. Alrazi Abdeljabbar
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  2. M. Belal Hossen
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  3. Harun-Or Roshid
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  4. Abdullah Aldurayhim
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Correspondence to Alrazi Abdeljabbar or Harun-Or Roshid.

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Abdeljabbar, A., Hossen, M.B., Roshid, HO. et al. Interactions of rogue and solitary wave solutions to the (2 + 1)-D generalized Camassa–Holm–KP equation. Nonlinear Dyn 110, 3671–3683 (2022). https://doi.org/10.1007/s11071-022-07792-x

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