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The discrete Korteweg-de Vries equation

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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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Authors and Affiliations

  1. Department of Applied Mathematical Sciences, University of Leeds, LS2 9JT, Leeds, UK

    Frank Nijhoff

  2. Institute of Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE, Amsterdam, The Netherlands

    Hans Capel

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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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