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Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation

Author

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  • Sivenathi Oscar Mbusi

    (Department of Mathematical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa)

  • Ben Muatjetjeja

    (Department of Mathematical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
    Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana)

  • Abdullahi Rashid Adem

    (Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria 0003, South Africa)

Abstract

The aim of this paper is to compute the exact solutions and conservation of a generalized (1 + 1) dimensional system. This can be achieved by employing symbolic manipulation software such as Maple, Mathematica, or MATLAB. In theoretical physics and in many scientific applications, the mentioned system naturally arises. Time, space, and scaling transformation symmetries lead to novel similarity reductions and new exact solutions. The solutions obtained include solitary waves and cnoidal and snoidal waves. The familiarity of closed-form solutions of nonlinear ordinary and partial differential equations enables numerical solvers and supports stability analysis. Although many efforts have been dedicated to solving nonlinear evolution equations, there is no unified method. To the best of our knowledge, this is the first time that Lie point symmetry analysis in conjunction with an ansatz method has been applied on this underlying equation. It should also be noted that the methods applied in this paper give a unique solution set that differs from the newly reported solutions. In addition, we derive the conservation laws of the underlying system. It is also worth mentioning that this is the first time that the conservation laws for the equation under study are derived.

Suggested Citation

  • Sivenathi Oscar Mbusi & Ben Muatjetjeja & Abdullahi Rashid Adem, 2021. "Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation," Mathematics, MDPI, vol. 9(22), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2916-:d:680118
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    References listed on IDEAS

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    1. Ma, Yu-Lan & Wazwaz, Abdul-Majid & Li, Bang-Qing, 2021. "A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 505-519.
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