SIGMA 1 (2005), 026, 6 pages nlin.SI/0512021
Conservation Laws of Discrete Korteweg-de Vries Equation
Olexandr G. Rasin and Peter E. Hydon
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK
Received October 21, 2005, in final form December 06, 2005; Published online December 09, 2005
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.
conservation laws; discrete equations; quad-graph.
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- Adler V.E., Bobenko A.I., Suris Yu.B.,
Classification of integrable equations on quad-graphs. The consistency approach,
Comm. Math. Phys., 2003, V.233, 513-543, nlin.SI/0202024.
- Hirota R.,
Nonlinear partial difference equations. I. A difference analog
of the Kortewega-de Vries equation, J. Phys. Soc. Japan,
1977, V.43, 1423-1433.
- Hydon P.E., Conservation laws of partial difference equations with two independent variables,
J. Phys. A: Math. Gen., 2001, V.34, 10347-10355.