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M-lump, interaction between lumps and stripe solitons solutions to the (2+1)-dimensional KP-BBM equation

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Abstract

In this paper, we have earned the M-lump solutions, the interaction within stripe solitons and lumps which are more considered mentioning that lumps will be drowned or swallowed by the stripe solitons. By utilizing the Hirota bilinear method and via the symbolic calculations, solve the (\(2+1\))-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. We obtain some multiple collisions of lumps. Next, the interactive solutions between M-lumps and N-stripe solitons have very enhanced the existing literature on the KP-BBM equation. Through the three-dimensional plots, contour, and two-dimensional plots by utilizing Maple software, the physical properties of these waves are described very well. That will be extensively used to describe many interesting physical phenomena in the areas of gas, plasma, optics, acoustics, heat transfer, fluid dynamics, classical mechanics, and so on. These new results can help us better understand interesting physical phenomena and mechanisms.

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Acknowledgements

The authors would like to thank the given comments and valuable recommendations by respected reviewer provided to improve the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran

    Jalil Manafian

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

    Muhammad Amin S. Murad

  3. Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran

    As’ad Alizadeh

  4. Department of Mechanical Engineering, College of Engineering, University of Zakho, Zakho, Iraq

    As’ad Alizadeh

  5. Department of Mechanical Engineering, Urmia University, Urmia, Iran

    Samad Jafarmadar

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  1. Jalil Manafian
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  2. Muhammad Amin S. Murad
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  4. Samad Jafarmadar
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Correspondence to Jalil Manafian.

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Manafian, J., Murad, M.A.S., Alizadeh, A. et al. M-lump, interaction between lumps and stripe solitons solutions to the (2+1)-dimensional KP-BBM equation. Eur. Phys. J. Plus 135, 167 (2020). https://doi.org/10.1140/epjp/s13360-020-00109-0

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