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A recursion operator is constructed for a new integrable system of coupled Korteweg–de Vries equations by the method of gauge-invariant description of zero-curvature representations. This second-order recursion operator is characterized by unusual structure of its nonlocal part. [ABSTRACT FROM AUTHOR]

The paper contains five examples of using cyclic bases of zero-curvature representations in studies of weak and strong Lax pairs, hierarchies of evolution systems, and recursion operators. [ABSTRACT FROM AUTHOR]