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arXiv · 1211.6958

Integrability of reductions of the discrete KdV and potential KdV equations

A. N. W. Hone·P. H. van der Kamp·G. R. W. Quispel·D. T. Tran
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Abstract

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.

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A. N. W. Hone, P. H. van der Kamp, G. R. W. Quispel, D. T. Tran. 2013-03-21. Integrability of reductions of the discrete KdV and potential KdV equations. https://doi.org/10.1098/rspa.2012.0747

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