Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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.

Key words: conservation laws; discrete equations; quad-graph.

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