{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T00:33:48Z","timestamp":1761352428255,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,8]],"date-time":"2022-01-08T00:00:00Z","timestamp":1641600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature.<\/jats:p>","DOI":"10.3390\/sym14010108","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Symmetries and Solvability of a Class of Higher Order Systems of Ordinary Difference Equations"],"prefix":"10.3390","volume":"14","author":[{"given":"Kgatliso","family":"Mkhwanazi","sequence":"first","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3046-0679","authenticated-orcid":false,"given":"Mensah","family":"Folly-Gbetoula","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2307\/3619976","article-title":"Evolution of the idea of symmetry in the nineteenth century, by IM Yaglom. 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Mathematical Modelling in One Dimension: An Introduction via Difference and Differential Equation, Cambridge University Press.","DOI":"10.1017\/CBO9781139565370"},{"key":"ref_11","first-page":"356","article-title":"Solutions and formulae for some systems of difference equations","volume":"1","author":"Almatrafi","year":"2018","journal-title":"MathLAB J."},{"key":"ref_12","first-page":"355","article-title":"Analysis of Solutions of Some Discrete Systems of Rational Difference Equations","volume":"29","author":"Almatrafi","year":"2020","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1080\/10236198.2020.1718667","article-title":"A generalised two-dimensional system of higher order recursive sequences","volume":"26","author":"Nyirenda","year":"2020","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hydon, P.E. (2000). Symmetry Methods for Differential Equations: A Beginner\u2019s Guide, Cambridge University Press.","DOI":"10.1017\/CBO9780511623967"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1006\/jmaa.1995.1393","article-title":"The existence of Lie Symmetries for First-Order Analytic Discrete Dynamical Systems","volume":"195","author":"Joshi","year":"1995","journal-title":"J. Math. Anal. 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