Symmetry Lie algebra and exact solutions of some fourth-order difference equations

Abstract

In this paper, all the Lie point symmetries of difference equations of the form u n+4 = u n A n + B n u n u n+2 , where, (A n) n 0 and (B n) n 0 are sequences of real numbers, are obtained. We perform reduction of order using the invariant of the group of transformations. Furthermore, we obtain their solutions. In particular, our work generalizes some results in the literature.

On a Study of a Family of Higher-Order Recurrence Relations

“…is paper is a generalization of some work in [8,9,[12][13][14][15][16][17]. In fact, substituting l � 1, k � 2, a � 1 and b � ± 1 in (33), we obtain results in eorems 1 and 3 by Ibrahim in [15].…”

“…Lastly, it is worth indicating that some of the results in [8,9,15] have been studied in a more general setting by Folly-Gbetoula and Nyirenda in [12][13][14]16].…”

“…Special cases of (4) attracted the interest of many researchers and interesting results can be found in the literature, see [7][8][9][10][11][12][13][14][15][16][17] among others. In this paper, we generalize some results in these articles by studying (2) with initial values x 0 , x 1 , .…”

“…Examples of the use of difference equations in real-life include modeling the proliferation of disease, loan payments, population studies, etc. Recurrence equations of a general order have been investigated in the literature and from different approaches by several authors [3][4][5][6][7][8][9][10][11][12]. In their work, Almatrafi and others [8] discussed the exact solutions, stability, oscillation and periodic aspects of the the difference equations…”

Smiley Theorem for Spectral Operators Whose Radical Part Is Locally Nilpotent

“…This is also partially motivated by the first author's study on the long-standing classification problem for quasi-finite representations of Lie algebras of vector fields (cf. [6]), which plays an important role in symmetry analysis for mathematics and physics (see, e.g., [7][8][9]).…”