Integrability of reductions of the discrete KdV and potential KdV   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 Korteweg-de Vries equation (pKdV). 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. The mappings associated with two copies of the pKdV equation are also shown to be integrable. 
A.N.W. Hone, P.H. van der Kamp, G.R.W. Quispel and D.T. Tran
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