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

Mnguni, N. ¹ ; Nyirenda, D. ¹ ; Folly-Gbetoula, M. ¹

¹ School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 11, p. 1262-1270.

Résumé

In this paper, all the Lie point symmetries of difference equations of the form

$ u_{n+4}=\frac{u_n}{A_n +B_nu_nu_{n+2}}, $

where, $(A_n)_{n \geq 0}$ and $(B_n)_{n \geq 0}$ 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.

Détail

DOI : 10.22436/jnsa.011.11.06

Classification : 39A10, 39A99, 39A13
Keywords: Difference equation, symmetry, group invariant solutions

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