FORM OF THE SOLUTIONS OF DIFFERENCE EQUATIONS VIA LIE SYMMETRY ANALYSIS AND FIBONACCI NUMBERS

被引:0
|
作者
Gocen, Melih [1 ]
Folly-Gbetoula, Mensah [2 ]
机构
[1] Ecevit Univ, Fac Sci, Dept Math, Zonguldak Bulent, Zonguldak, Turkiye
[2] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa
关键词
Difference equation; form of the solutions; reduction; Lie symmetry analysis; Fibonacci numbers; BEHAVIOR; DYNAMICS; SYSTEMS; TERMS;
D O I
10.2989/16073606.2023.2229520
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we give the form of the solutions of the following rational difference equation x(n+1) = x(n-3)x(n-1)/a(n)x(n-3)+b(n)x(n-1), (1) where a(n) and b(n) are sequences of real numbers, by using Lie symmetry analysis and associated with Fibonacci numbers, respectively. We find an interesting relation between the exact solution of Equation (1) and the classical Fibonacci sequence.
引用
收藏
页码:399 / 411
页数:13
相关论文
共 50 条
  • [41] Lie-Backlund Symmetry, Reduction, and Solutions of Nonlinear Evolutionary Equations
    Rzeszut, W.
    Tsyfra, I. M.
    Vladimirov, V. A.
    UKRAINIAN MATHEMATICAL JOURNAL, 2022, 74 (03) : 385 - 394
  • [42] Lie group symmetry classification of solutions to coupled nonlinear Schrodinger equations
    Pulov, Vladimir I.
    Uzunov, Ivan M.
    Chacarov, Edy J.
    Lyutskanov, Valentin L.
    14TH INTERNATIONAL SCHOOL ON QUANTUM ELECTRONICS: LASER PHYSICS AND APPLICATIONS, 2007, 6604
  • [43] Lie–Bäcklund Symmetry, Reduction, and Solutions of Nonlinear Evolutionary Equations
    W. Rzeszut
    I. M. Tsyfra
    V. A. Vladimirov
    Ukrainian Mathematical Journal, 2022, 74 : 385 - 394
  • [44] Lie and non-Lie symmetry and some exact solutions of the self-dual equations
    Stognii, V
    REPORTS ON MATHEMATICAL PHYSICS, 1999, 44 (1-2) : 241 - 245
  • [45] Primary Branch Solutions of First Order Autonomous Scalar Partial Differential Equations via Lie Symmetry Approach
    Lou, S. Y.
    Yao, Ruo Xia
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2017, 24 (03) : 379 - 392
  • [46] Primary Branch Solutions of First Order Autonomous Scalar Partial Differential Equations via Lie Symmetry Approach
    S. Y. Lou
    Ruo Xia Yao
    Journal of Nonlinear Mathematical Physics, 2017, 24 : 379 - 392
  • [47] Lie symmetry analysis, exact analytical solutions and dynamics of solitons for (2 + 1)-dimensional NNV equations
    Kumar S.
    Niwas M.
    Wazwaz A.-M.
    Phys Scr, 2020, 9
  • [48] Lie symmetry analysis, analytical solutions and conservation laws to the coupled time fractional variant Boussinesq equations
    Liu, Wenhao
    Zhang, Yufeng
    WAVES IN RANDOM AND COMPLEX MEDIA, 2021, 31 (01) : 182 - 197
  • [49] Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations
    Liu, Hanze
    Li, Jibin
    Liu, Lei
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 368 (02) : 551 - 558
  • [50] Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrodinger equations
    Bai, Yu-Shan
    Liu, Ya-Na
    Ma, Wen-Xiu
    NONLINEAR DYNAMICS, 2023, 111 (19) : 18439 - 18448