Geodesic
Conservation Laws of Discrete Korteweg–de Vries Equation
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

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All three-point and five-point conservation laws for the discrete Korteweg–de Vries equations are found. These conservation laws satisfy a functional equation, which we solve by reducing it to a system of partial differential equations. Our method uses computer algebra intensively, because the determining functional equation is quite complicated.
Keywords: conservation laws; discrete equations; quad-graph. 
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     author = {Olexandr G. Rasin and Peter E. Hydon},
     title = {Conservation {Laws} of {Discrete} {Korteweg{\textendash}de~Vries} {Equation}},
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Olexandr G. Rasin; Peter E. Hydon. Conservation Laws of Discrete Korteweg–de Vries Equation. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a25/

[1] Adler V. E., Bobenko A. I., Suris Yu. B., “Classification of integrable equations on quad-graphs. The consistency approach”, Comm. Math. Phys., 233 (2003), 513–543 ; arXiv:nlin.SI/0202024 | MR | Zbl

[2] Hirota R., “Nonlinear partial difference equations. I. A difference analog of the Korteweg–de Vries equation”, J. Phys. Soc. Japan, 43 (1977), 1423–1433 | MR

[3] Hydon P. E., “Conservation laws of partial difference equations with two independent variables”, J. Phys. A: Math. Gen., 34 (2001), 10347–10355 | DOI | MR | Zbl