Integrability of reductions of the discrete Korteweg-de Vries and potential Korteweg-de Vries equations

We study the integrability of mappings obtained as reductions of the discrete Korteweg-de Vries (KdV) equation and of two copies of the discrete potential KdV (pKdV) equation. We show that the mappings corresponding to the discrete KdV equation, which can be derived from the latter, are completely integrable in the Liouville-Arnold sense. Themappings associated with two copies of the pKdV equation are also shown to be integrable.