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TMF, 2011, Volume 168, Number 1, Pages 24–34 (Mi tmf6661)  

This article is cited in 9 scientific papers (total in 9 papers)

Classical and nonclassical symmetries for the Krichever–Novikov equation

M. S. Bruzón, M. L. Gandarias

Departamento de Matemáticas, Universidad de Cádiz, Cádiz, Spain

Abstract: We study the Krichever–Novikov equation from the standpoint of the theory of symmetry reductions in partial differential equations. We obtain a Lie group classification. Moreover, we obtain some exact solutions, and we apply the nonclassical method.

Keywords: partial differential equation, symmetry, exact solution

DOI: https://doi.org/10.4213/tmf6661

Full text: PDF file (480 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 875–885

Bibliographic databases:


Citation: M. S. Bruzón, M. L. Gandarias, “Classical and nonclassical symmetries for the Krichever–Novikov equation”, TMF, 168:1 (2011), 24–34; Theoret. and Math. Phys., 168:1 (2011), 875–885

Citation in format AMSBIB
\Bibitem{BruGan11}
\by M.~S.~Bruz\'on, M.~L.~Gandarias
\paper Classical and nonclassical symmetries for the~Krichever--Novikov equation
\jour TMF
\yr 2011
\vol 168
\issue 1
\pages 24--34
\mathnet{http://mi.mathnet.ru/tmf6661}
\crossref{https://doi.org/10.4213/tmf6661}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2021731}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011TMP...168..875B}
\transl
\jour Theoret. and Math. Phys.
\yr 2011
\vol 168
\issue 1
\pages 875--885
\crossref{https://doi.org/10.1007/s11232-011-0073-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79961163722}


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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. Bruzón M.S., Gandarias M.L., “Symmetry reductions and traveling wave solutions for the Krichever-Novikov equation”, Math. Methods Appl. Sci., 35:8 (2012), 869–876  crossref  mathscinet  zmath  isi  elib  scopus
    2. Gupta R.K., Bansal A., “Painlevé analysis, Lie symmetries and invariant solutions of potential Kadomstev–Petviashvili equation with time dependent coefficients”, Appl. Math. Comput., 219:10 (2013), 5290–5302  crossref  mathscinet  zmath  isi  scopus
    3. 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  scopus
    4. Camacho J.C., Rosa M., Gandarias M.L., Bruzon M.S., “Classical symmetries, travelling wave solutions and conservation laws of a generalized Fornberg?Whitham equation”, J. Comput. Appl. Math., 318:SI (2017), 149–155  crossref  mathscinet  zmath  isi  scopus
    5. Najafi R., Bahrami F., Hashemi M.S., “Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations”, Nonlinear Dyn., 87:3 (2017), 1785–1796  crossref  mathscinet  zmath  isi  scopus
    6. Bahrami F., Najafi R., Hashemi M.S., “On the Invariant Solutions of Space/Time-Fractional Diffusion Equations”, Indian J. Phys., 91:12 (2017), 1571–1579  crossref  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. Rosa M., Carlos Camacho J., Bruzon M., Luz Gandarias M., “Lie Symmetries and Conservation Laws For a Generalized Kuramoto-Sivashinsky Equation”, Math. Meth. Appl. Sci., 41:17, SI (2018), 7295–7303  crossref  mathscinet  zmath  isi
    9. Camacho J.C., Rosa M., Gandarias M.L., Bruzon M.S., “Classical Symmetries and Conservation Laws For the Dissipative Dullin-Gottwald-Holm Equation With Arbitrary Coefficients”, Math. Meth. Appl. Sci., 41:17, SI (2018), 7304–7312  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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