LIE GROUP ANALYSIS OF FRACTAL DIFFERENTIAL-DIFFERENCE EQUATIONS

Yan Wang, Li Xu, Yu-Jin Wang and Jian-Gen Liu
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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

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-7

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.

Keywords: Lattice Problem; Two-Scale Fractal; Lie Group Analysis; The Differential-Difference Burgers Equation; The Klein–Gordon Equation; Analytical Solutions; Two-Scale Transform (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501978

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