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Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

Author

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  • Innocent Simbanefayi

    (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)

  • 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, China
    Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli str., 71, Baku AZ1007, Azerbaijan)

Abstract

In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this paper are the most general since they contain elliptic functions. Finally, we derive the conserved quantities of this equation by employing two approaches—the general multiplier approach and Ibragimov’s theorem. The importance of conservation laws is explained in the introduction. It should be pointed out that the investigation of higher dimensional nonlinear partial differential equations is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.

Suggested Citation

  • Innocent Simbanefayi & Chaudry Masood Khalique, 2020. "Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1012-:d:374112
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    References listed on IDEAS

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    1. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
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