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SIGMA, 2011, Volume 7, 097, 16 pages (Mi sigma655)  

This article is cited in 8 scientific papers (total in 8 papers)

Symmetries of the Continuous and Discrete Krichever–Novikov Equation

Decio Levia, Pavel Winternitzb, Ravil I. Yamilovc

a Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and Sezione INFN, Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
b Centre de recherches mathématiques and Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, H3C 3J7, Montréal (Québec), Canada
c Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russian Federation

Abstract: A symmetry classification is performed for a class of differential-difference equations depending on $9$ parameters. A $6$-parameter subclass of these equations is an integrable discretization of the Krichever–Novikov equation. The dimension $n$ of the Lie point symmetry algebra satisfies $1\le n\le 5$. The highest dimensions, namely $n=5$ and $n=4$ occur only in the integrable cases.

Keywords: symmetry classification, integrable PDEs, integrable differential-difference equations.

DOI: https://doi.org/10.3842/SIGMA.2011.097

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Full text: http://emis.mi.ras.ru/.../097
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Bibliographic databases:

ArXiv: 1110.5021
MSC: 35B06; 35K25; 37K10; 39A14
Received: June 16, 2011; in final form October 15, 2011; Published online October 23, 2011
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Citation: Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.

Citation in format AMSBIB
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\by Decio Levi, Pavel Winternitz, Ravil I. Yamilov
\paper Symmetries of the Continuous and Discrete Krichever--Novikov Equation
\jour SIGMA
\yr 2011
\vol 7
\papernumber 097
\totalpages 16
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Demskoi D.K., Viallet C.-M., “Algebraic Entropy for Semi-Discrete Equations”, J. Phys. A-Math. Theor., 45:35 (2012), 352001  crossref  mathscinet  zmath  isi  elib  scopus
    2. Levi D., Scimiterna Ch., “Classification of Multilinear Real Quadratic Partial Difference Equations Linearizable by Point and Hopf-Cole Transformations”, Int. J. Geom. Methods Mod. Phys., 9:2, SI (2012), 1260004  crossref  mathscinet  isi  scopus
    3. Levi D., Ricca E., Thomova Z., Winternitz P., “Lie Group Analysis of a Generalized Krichever-Novikov Differential-Difference Equation”, J. Math. Phys., 55:10 (2014), 103503  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Gungor F., Ozemir C., “Lie Symmetries of a Generalized Kuznetsov-Zabolotskaya-Khokhlov Equation”, J. Math. Anal. Appl., 423:1 (2015), 623–638  crossref  mathscinet  zmath  isi  elib  scopus
    5. Anco S.C., Avdonina E.D., Gainetdinova A., Galiakberova L.R., Ibragimov N.H., Wolf T., “Symmetries and Conservation Laws of the Generalized Krichever-Novikov Equation”, J. Phys. A-Math. Theor., 49:10, SI (2016), 105201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Gubbiotti G., Scimiterna C., Levi D., “The Non-Autonomous Ydkn Equation and Generalized Symmetries of Boll Equations”, J. Math. Phys., 58:5 (2017), 053507  crossref  mathscinet  zmath  isi  scopus
    7. Kou K., Li J., “Exact Traveling Wave Solutions of the Krichever-Novikov Equation: a Dynamical System Approach”, Int. J. Bifurcation Chaos, 27:4 (2017), 1750058  crossref  mathscinet  zmath  isi  scopus
    8. Habibullin I.T., Khakimova A.R., “On the Recursion Operators For Integrable Equations”, J. Phys. A-Math. Theor., 51:42 (2018), 425202  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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