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Group Analysis Of The Time Fractional (3 + 1)-Dimensional Kdv-Type Equation

Author

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  • JIAN-GEN LIU

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

  • XIAO-JUN YANG

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China‡School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

  • LU-LU GENG

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

  • YU-RONG FAN

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

Abstract

Under investigations into this paper is a higher-dimensional model, namely the time fractional (3 + 1)-dimensional Korteweg–de Vries (KdV)-type equation, which can be usually used to express shallow water wave phenomena. At the beginning, the symmetry of the time fractional (3 + 1)-dimensional KdV-type equation via the group analysis scheme is obtained. The definition of the fractional derivative in the sense of the Riemann–Liouville is considered. Then, the one-parameter Lie group and invariant solutions of this considered equation are constructed. Subsequently, we applied a direct method to construct the optimal system of one-dimensional of this considered equation. Next, this considered higher-dimensional model can be reduced into the lower-dimensional fractional differential equations (FDEs) with the help of the three-parameter and two-parameter Erdélyi–Kober fractional differential operators (FDOs). Lastly, conservation laws of this discussed equation by using a new conservation theorem are also found. A series of results of the above obtained can provide strong support for us to reveal the mysterious veil of this viewed equation.

Suggested Citation

  • Jian-Gen Liu & Xiao-Jun Yang & Lu-Lu Geng & Yu-Rong Fan, 2021. "Group Analysis Of The Time Fractional (3 + 1)-Dimensional Kdv-Type Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-19, September.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:06:n:s0218348x21501693
    DOI: 10.1142/S0218348X21501693
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