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Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method

Author

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  • Xiaoming Wang

    (School of Mathematics & Computer Science, Shangrao Normal University, Shangrao 334001, China)

  • Shehbaz Ahmad Javed

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Abdul Majeed

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Mohsin Kamran

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Muhammad Abbas

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

Abstract

In this article, an analytical technique based on unified method is applied to investigate the exact solutions of non-linear homogeneous evolution partial differential equations. These partial differential equations are reduced to ordinary differential equations using different traveling wave transformations, and exact solutions in rational and polynomial forms are obtained. The obtained solutions are presented in the form of 2D and 3D graphics to study the behavior of the analytical solution by setting out the values of suitable parameters. The acquired results reveal that the unified method is a suitable approach for handling non-linear homogeneous evolution equations.

Suggested Citation

  • Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2996-:d:892587
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    References listed on IDEAS

    as
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    3. Ali, Khalid K. & Cattani, Carlo & Gómez-Aguilar, J.F. & Baleanu, Dumitru & Osman, M.S., 2020. "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Pshtiwan Othman Mohammed & José António Tenreiro Machado & Juan L. G. Guirao & Ravi P. Agarwal, 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
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