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


SIGMA 1 (2005), 026, 6 pages      nlin.SI/0512021      http://dx.doi.org/10.3842/SIGMA.2005.026

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

Abstract
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.

pdf (201 kb)   ps (216 kb)   tex (140 kb)

References

  1. 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.
  2. 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.
  3. Hydon P.E., Conservation laws of partial difference equations with two independent variables, J. Phys. A: Math. Gen., 2001, V.34, 10347-10355.

Previous article   Next article   Contents of Volume 1 (2005)