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Boiti–Leon–Manna–Pempinelli equation including time-dependent coefficient (vcBLMPE): a variety of nonautonomous geometrical structures of wave solutions

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Abstract

Our work aims to investigate the vcBLMPE in \((3+1)\)-dimensions (3D-vcBLMPE) that characterizes wave propagation in incompressible fluids. In real-world issues, nonlinear partial differential equations containing time-dependent coefficients are more relevant than those with constant coefficients owing to inhomogeneities of media and nonuniformities of boundaries. In shallow water, linearization of the wave formation needs more critical wave capacity criteria than in water depths, and the strongly nonlinear aspects are readily visible. By using symbolic computation, several nonautonomous wave solutions with different geometric structures are obtained. Each of the gained solutions is presented graphically based on various arbitrary coefficients to demonstrate and better comprehend their dynamical properties. As a comparison between the new results and the results previously reported, we have presented several completely new findings in this study.

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Data Availability Statement

All data generated or analyzed during this study are included in this published article.

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Acknowledgements

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4410172DSR13).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq

    H. F. Ismael

  2. Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey

    A. N. Akkilic & H. Bulut

  3. Department of of Mathematics, College of Science, University of Duhok, Duhok, Iraq

    M. A. S. Murad

  4. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    W. Mahmoud

  5. Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah, 21955, Saudi Arabia

    M. S. Osman

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  1. H. F. Ismael
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Correspondence to W. Mahmoud or M. S. Osman.

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Ismael, H.F., Akkilic, A.N., Murad, M.A.S. et al. Boiti–Leon–Manna–Pempinelli equation including time-dependent coefficient (vcBLMPE): a variety of nonautonomous geometrical structures of wave solutions. Nonlinear Dyn 110, 3699–3712 (2022). https://doi.org/10.1007/s11071-022-07817-5

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