A notion of symmetry for 1+1‐dimensional integrable systems is presented which is consistent with their group theoretic description. It is shown how a group symmetry may be used together with a dynamical reduction to produce new generalizations of the Bäcklund transformation for the Korteweg–de Vries equation to its SL(n,C) generalization. An additional application to the relativistic invariance of the Leznov–Saveliev systems is given.

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