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The \(\varvec{N}\)-soliton, fusion, rational and breather solutions of two extensions of the (2+1)-dimensional Bogoyavlenskii–Schieff equation

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Abstract

The aim of this work is to analyze and explore the dynamics of two extensions of the Bogoyavlenskii–Schieff equation. The Hirota bilinear method is applied to the equations that arise in plasma physics. The N-soliton, fusion, rational solutions and breather solutions, as well as the interaction between M-lump and soliton solutions, are retrieved for both extended equations. The M-lump wave solutions are created from the soliton wave solutions, which are established via the Hirota bilinear method, by considering a longwave limit to the soliton wave solutions and presenting suitable conjugation conditions. The solutions for a given choice of constants are represented graphically to better understand the associated physical phenomena such as the propagation behaviors and the types of collisions.

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Authors and Affiliations

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

    Hajar F. Ismael

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

    Hajar F. Ismael & Hasan Bulut

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

    M. S. Osman

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  1. Hajar F. Ismael
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  2. Hasan Bulut
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  3. M. S. Osman
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Correspondence to M. S. Osman.

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Ismael, H.F., Bulut, H. & Osman, M.S. The \(\varvec{N}\)-soliton, fusion, rational and breather solutions of two extensions of the (2+1)-dimensional Bogoyavlenskii–Schieff equation. Nonlinear Dyn 107, 3791–3803 (2022). https://doi.org/10.1007/s11071-021-07154-z

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