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Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science

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  • Chaudry Masood Khalique

    (International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
    College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
    Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli str., 71, Baku AZ1007, Azerbaijan)

  • Oke Davies Adeyemo

    (International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa)

Abstract

In this article, we examine a (3+1)-dimensional generalized breaking soliton equation which is highly applicable in the fields of engineering and nonlinear sciences. Closed-form solutions in the form of Jacobi elliptic functions of the underlying equation are derived by the method of Lie symmetry reductions together with direct integration. Moreover, the ( G ′ / G ) -expansion technique is engaged, which consequently guarantees closed-form solutions of the equation structured in the form of trigonometric and hyperbolic functions. In addition, we secure a power series analytical solution of the underlying equation. Finally, we construct local conserved vectors of the aforementioned equation by employing two approaches: the general multiplier method and Ibragimov’s theorem.

Suggested Citation

  • Chaudry Masood Khalique & Oke Davies Adeyemo, 2020. "Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1692-:d:422859
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    References listed on IDEAS

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    1. Mohamed R. Ali & Wen-Xiu Ma, 2019. "New Exact Solutions of Nonlinear (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-7, June.
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    4. Chen, Yong & Yan, Zhenya, 2005. "New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 399-406.
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    1. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.

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