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Lie Group Analysis Of Fractal Differential-Difference Equations

Author

Listed:
  • YAN WANG

    (School of Science, Tianjin, University of Commerce, Tianjin 300134, P. R. China†School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China)

  • LI XU

    (School of Science, Tianjin, University of Commerce, Tianjin 300134, P. R. China)

  • YU-JIN WANG

    (School of Science, Tianjin, University of Commerce, Tianjin 300134, P. R. China)

  • JIAN-GEN LIU

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

Abstract

A difference equation can well describe a lattice problem, and its dynamical property was always modeled approximately by a differential-difference equation. This paper suggests a fractal differential-difference model by taking into account the lattice’s geometry. The fractal differential-difference Burgers equation and the fractal Klein–Gordon equation are used as examples to study the solution properties by the Lie group method, and various Lie algebras of the corresponding Lie transformation group are also obtained.

Suggested Citation

  • Yan Wang & Li Xu & Yu-Jin Wang & Jian-Gen Liu, 2021. "Lie Group Analysis Of Fractal Differential-Difference Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-7, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21501978
    DOI: 10.1142/S0218348X21501978
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