The invariance and formulas for solutions of some fifth-order difference equations

2019/02/18 by Darlison Nyirenda, Nyirenda, D., Mensah Folly-Gbetoula +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1902.06482

openalex publication_date 2019/02/18 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

Lie group analysis of the difference equations of the form x_n+1 =\fracx_n-4x_n-3x_n(a_n +b_nx_n-4x_n-3x_n-2x_n-1), where a_n and b_n are real sequences, is performed and non-trivial symmetries are derived. Furthermore, we find find formulas for exact solutions of the equations. This work generalizes a recent result by Elsayed [Elsayed, E.M.: Expression and behavior of the solutions of some rational recursive sequences. Math. Meth. Appl. Sci. \bf 2016:39,5682--5694 (2016)].

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