Abstract
We review the different aspects of integrable discretizations in space and time of the Korteweg-de Vries equation, including Miura transformations to related integrable difference equations, connections to integrable mappings, similarity reductions and discrete versions of Painlevé equations as well as connections to Volterra systems.
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Nijhoff, F., Capel, H. The discrete Korteweg-de Vries equation. Acta Appl Math 39, 133–158 (1995). https://doi.org/10.1007/BF00994631
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DOI: https://doi.org/10.1007/BF00994631