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

journal contribution
posted on 29.03.2022, 06:24 by ANW Hone, Pieter Van Der KampPieter Van Der Kamp, Gilles QuispelGilles Quispel, DT Tran
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.

Funding

This work was supported by the Australian Research Council. D. T. T. visited the University of Kent in 2011 and 2012, and is grateful for the support of an Edgar Smith Scholarship which funded her travel. A.N.W.H. thanks the organizers of the Nonlinear Dynamical Systems workshop for supporting his trip to La Trobe University, Melbourne in September-October 2012.

History

Publication Date

08/06/2013

Journal

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volume

469

Issue

2154

Article Number

20120747

Pagination

23p.

Publisher

Royal Society Publishing

ISSN

1364-5021

Rights Statement

© The Royal Society 2013

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