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SIGMA, 2005, Volume 1, 026, 6 pp. (Mi sigma26)  

This article is cited in 13 scientific papers (total in 13 papers)

Conservation Laws of Discrete Korteweg–de Vries Equation

Olexandr G. Rasin, Peter E. Hydon

Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK

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.

Keywords: conservation laws; discrete equations; quad-graph

DOI: https://doi.org/10.3842/SIGMA.2005.026

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Full text: http://emis.mi.ras.ru/.../Paper026
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ArXiv: nlin.SI/0512021
MSC: 70H33; 37K10; 39A05
Received: October 21, 2005; in final form December 6, 2005; Published online December 9, 2005
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Citation: Olexandr G. Rasin, Peter E. Hydon, “Conservation Laws of Discrete Korteweg–de Vries Equation”, SIGMA, 1 (2005), 026, 6 pp.

Citation in format AMSBIB
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\by Olexandr G. Rasin, Peter E. Hydon
\paper Conservation Laws of Discrete Korteweg--de~Vries Equation
\jour SIGMA
\yr 2005
\vol 1
\papernumber 026
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\crossref{https://doi.org/10.3842/SIGMA.2005.026}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rasin, OG, “Conservation laws for NQC-type difference equations”, Journal of Physics A-Mathematical and General, 39:45 (2006), 14055  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Maruno K.-I., Quispel G. R. W., “Construction of integrals of higher-order mappings”, Journal of the Physical Society of Japan, 75:12 (2006), 123001  crossref  mathscinet  adsnasa  isi  scopus
    3. Rasin O.G., Hydon P.E., “Conservation laws for integrable difference equations”, Journal of Physics A-Mathematical and Theoretical, 40:42 (2007), 12763–12773  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Rasin O.G., Hydon P.E., “Symmetries of integrable difference equations on the quad-graph”, Studies in Applied Mathematics, 119:3 (2007), 253–269  crossref  mathscinet  isi  scopus
    5. Sahadevan R., Rasin O.G., Hydon P.E., “Integrability conditions for nonautonomous quad-graph equations”, Journal of Mathematical Analysis and Applications, 331:1 (2007), 712–726  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Rasin A.G., Schiff J., “Infinitely many conservation laws for the discrete KdV equation”, Journal of Physics A-Mathematical and Theoretical, 42:17 (2009), 175205  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Rasin A.G., “Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method”, Journal of Physics A-Mathematical and Theoretical, 43:23 (2010), 235201  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Maheswari C.U., Sahadevan R., “On the conservation laws for nonlinear partial difference equations”, Journal of Physics A-Mathematical and Theoretical, 44:27 (2011), 275203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Folly-Gbetoula M.K., Kara A.H., “Symmetries, Conservation Laws, and ‘Integrability’ of Difference Equations”, Adv. Differ. Equ., 2014, 224  crossref  mathscinet  isi  scopus
    10. Ndlovu L., Folly-Gbetoula M., Kara A.H., Love A., “Symmetries, Associated First Integrals, and Double Reduction of Difference Equations”, Abstract Appl. Anal., 2014, 490165  crossref  mathscinet  isi  scopus
    11. Folly-Gbetoula M., Kara A.H., “Invariance analysis and reduction of discrete Painlevé equations”, J. Differ. Equ. Appl., 22:9 (2016), 1378–1388  crossref  mathscinet  zmath  isi  scopus
    12. Hietarinta J. Joshi N. Nijhoff F., “Discrete Systems and Integrability”, Discrete Systems and Integrability, Cambridge Texts in Applied Mathematics, Cambridge Univ Press, 2016, 1–445  mathscinet  zmath  isi
    13. Lou S. Shi Y. Zhang D.-j., “Spectrum transformation and conservation laws of lattice potential KdV equation”, Front. Math. China, 12:2 (2017), 403–416  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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