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Dynamical Behavior of Traveling Wave Solutions for a (2+1)-Dimensional Bogoyavlenskii Coupled System

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Abstract

In this paper, we applied some computational tools, namely the modified extended tanh method via a Riccati equation, the general Exp\(_{a}\)-function method and the bifurcation methods to study a nonlinear (2+1)-dimensional Bogoyavlenskii coupled system in thin-film ferroelectric medium to construct exact traveling wave solutions. By applying a classical wave transformation we obtained an ordinary differential equations. As a result, some new traveling wave solutions are obtained including hyperbolic, trigonometric, exponential functions and rational forms. If the parameters take specific values, then the periodic wave, solitary waves, kink and anti-kink wave solutions are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special cases of these nonlinear equations by the help of programming language Maple.

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Authors and Affiliations

  1. Nanjing University of Information Science and Technology, 219 Ningliu Road, Nanjing, 210044, People’s Republic of China

    Temesgen Desta Leta & Wenjun Liu

  2. Department of Mathematics, Dilla University, 419, Dilla, Ethiopia

    Temesgen Desta Leta

  3. Department of Mathematics, Faculty of Sciences, University Cadi Ayyad Bd. du Prince Moulay Abdellah, B.P. 2390, Marrakech, Morocco

    Abdelfattah El Achab

  4. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  5. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, Turkey

    Ahmet Bekir

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  1. Temesgen Desta Leta
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  2. Wenjun Liu
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  3. Abdelfattah El Achab
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  4. Hadi Rezazadeh
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Correspondence to Ahmet Bekir.

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The first author is supported by Talented Young Scientist Program of Ministry of Science and Technology of China (Ethiopia-18-010) and National Natural Science Foundation of China (11950410502). The second author is supported by National Natural Science Foundation of China (11771216, 11301277), the Six Talent Peaks Project in Jiangsu Province [(2015-XCL-020).

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Leta, T.D., Liu, W., Achab, A.E. et al. Dynamical Behavior of Traveling Wave Solutions for a (2+1)-Dimensional Bogoyavlenskii Coupled System. Qual. Theory Dyn. Syst. 20, 14 (2021). https://doi.org/10.1007/s12346-021-00449-x

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