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General form of the solutions of some difference equations via Lie symmetry analysis

Dynamical Systems 2019-10-16 v1 Exactly Solvable and Integrable Systems

Abstract

In this paper, we obtain exact solutions of the following rational difference equation xn+1=xnxn2xn4xn1xn3(an+bnxnxn2xn4), x_{n+1}=\frac{x_{n}x_{n-2}x_{n-4}}{ x_{n-1}x_{n-3}(a_{n}+b_{n}x_{n}x_{n-2}x_{n-4})}, where ana_{n} and bnb_{n} are random real sequences, by using the technique of Lie symmetry analysis. Moreover, we discuss the periodic nature and behavior of solutions for some special cases. This work is a generalization of some works by Elsayed and Ibrahim in [E.M.Elsayed, T. F. Ibrahim, { Solutions and periodicity of a rational recursive sequences of order five}, Bulletin of the Malaysian Mathematical Sciences Society 38:1 (2015), 95-112].

Keywords

Cite

@article{arxiv.1910.06880,
  title  = {General form of the solutions of some difference equations via Lie symmetry analysis},
  author = {Mensah Folly-Gbetoula and Melih Göcen and Miraç Güneysu},
  journal= {arXiv preprint arXiv:1910.06880},
  year   = {2019}
}

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