Gürses, MetinPekcan, Aslı2025-02-172025-02-172025-01-0703759601https://hdl.handle.net/11693/116324In this work we generalize M2-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M3-extensions of the KdV equation and their recursion operators. We give a compact form of Mn-extension of the KdV equation and recursion operator of the coupled KdV system. The method of Mn-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M3-extension of KdV.EnglishCC BY-NC-ND 4.0 DEED (Attribution-NonCommercial-NoDerivatives 4.0 International)https://creativecommons.org/licenses/by-nc-nd/4.0/deed.enCoupled systemsIntegrabilityMn-extensionNonlocal reductionsRecursion operatorArticle10.1016/j.physleta.2024.130217