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Symmetry Scheme Of The Time Fractional (3 + 1)-Dimensional Modified Extended Zakharov–Kuznetsov Equation In Plasma Physics

Author

Listed:
  • JIAN-GEN LIU

    (School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, P. R. China†Qin Institute of Mathematics, Shanghai Hanjing Centre for Science and Technology, Yexie Town, Songjiang District, Shanghai 201609, P. R. China)

  • BIN-LU FENG

    (��School of Mathematics and Information Sciences, Weifang University, Weifang 261000, Shandong, P. R. China)

  • YU-FENG ZHANG

    (�School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

Abstract

Higher-dimensional nonlinear models can describe more complex evolutionary mechanisms. In this paper, we considered the time fractional (3 + 1)-dimensional modified extended Zakharov–Kuznetsov equation with the sense of the Riemann–Liouville fractional derivative in plasma physics. In the first place, the existence of symmetry of this studied equation through the symmetry scheme was proved. Then, the optimal system to the time fractional (3 + 1)-dimensional modified extended Zakharov–Kuznetsov equation was also constructed. Subsequently, the time fractional higher-dimensional equation was reduced into the lower-dimensional fractional differential equation with the help of the Erdélyi–Kober fractional operators. Last, some conservation laws by using a new conservation theorem were also given. These novel results provide a window for us to discover this high-dimensional nonlinear equation.

Suggested Citation

  • Jian-Gen Liu & Bin-Lu Feng & Yu-Feng Zhang, 2025. "Symmetry Scheme Of The Time Fractional (3 + 1)-Dimensional Modified Extended Zakharov–Kuznetsov Equation In Plasma Physics," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-11.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:01:n:s0218348x25500045
    DOI: 10.1142/S0218348X25500045
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