Group Analysis of Generalized Fifth-Order Korteweg–de Vries Equations with Time-Dependent Coefficients

  • Oksana Kuriksha
  • Severin Pošta
  • Olena Vaneeva
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)


We perform enhanced Lie symmetry analysis of generalized fifth-order Korteweg–de Vries equations with time-dependent coefficients. The corresponding similarity reductions are classified and some exact solutions are constructed.


Group Classification Vries Equation Equivalence Transformation Determine Equation Point Transformation 
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The authors would like to thank the Organizing Committee of LT-10 and especially Prof. Vladimir Dobrev for the hospitality. O.K. and O.V. acknowledge the provided support for their participation in the Workshop. The authors are also grateful to Vyacheslav Boyko and Roman Popovych for useful discussions.


  1. 1.
    Bihlo, A., Dos Santos Cardoso-Bihlo, E., Popovych, R.O.: J. Math. Phys. 53, 123515 (2012)CrossRefGoogle Scholar
  2. 2.
    Cheviakov, A.F.: Comp. Phys. Commun. 176, 48–61 (2007)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Jeffrey, A., Kakutani, T.: SIAM Rev. 14, 582–643 (1972)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Kakutani, T., Ono, H.: J. Phys. Soc. Jpn. 26, 1305–1318 (1969)CrossRefGoogle Scholar
  5. 5.
    Kingston, J.G., Sophocleous, C.: J. Phys. A 31, 1597–1619 (1998)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Kuriksha, O., Pošta, S., Vaneeva, O.: J. Phys. A 47, 045201 (2014)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kuriksha, O., Pošta, S., Vaneeva, O.: Phys. Part. Nuc. Lett. 11(7), 6 (2014)Google Scholar
  8. 8.
    Olver, P.: Applications of Lie Groups to Differential Equations, 2nd edn. Springer, New York (1993)CrossRefMATHGoogle Scholar
  9. 9.
    Ovsiannikov, L.V.: Group Analysis of Differential Equations, 1st edn. Academic, New York (1982)MATHGoogle Scholar
  10. 10.
    Parkes, E.J., Duffy, B.R.: Comput. Phys. Commun. 98, 288–300 (1996)CrossRefMATHGoogle Scholar
  11. 11.
    Patera, J., Winternitz, P.: J. Math. Phys. 18, 1449–1455 (1977)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Popovych, R.O., Bihlo, A.: J. Math. Phys. 53, 073102 (2012)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Popovych, R.O., Kunzinger, M., Eshraghi, H.: Acta Appl. Math. 109, 315–359 (2010)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Vaneeva, O.: Commun. Nonlinear Sci. Numer. Simulat. 17, 611–618 (2012)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Vaneeva, O.O., Popovych, R.O., Sophocleous, C.: Phys. Scr. 89, 038003 (2014)CrossRefGoogle Scholar
  16. 16.
    Vaneeva, O.O., Papanicolaou, N.C., Christou, M.A., Sophocleous, C.: Commun. Nonlinear Sci. Numer. Simulat. 19, 3074–3085 (2014)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Wang, G.W., Xu, T.Z.: Abstr. Appl. Anal. 2013, 139160 (2013)Google Scholar
  18. 18.
    Wang, G.W., Liu, X.Q., Zhang, Y.Y.: J. Appl. Math. Inf. 31, 229–239 (2013)MATHMathSciNetGoogle Scholar
  19. 19.
    Winternitz, P., Gazeau, J.-P.: Phys. Lett. A167, 246–250 (1992)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Oksana Kuriksha
    • 1
  • Severin Pošta
    • 2
  • Olena Vaneeva
    • 3
  1. 1.Petro Mohyla Black Sea State UniversityMykolaivUkraine
  2. 2.Department of MathematicsFaculty of Nuclear Sciences and Physical Engineering, Czech Technical University in PraguePragueCzech Republic
  3. 3.Institute of Mathematics of the National Academy of Sciences of UkraineKyiv-4Ukraine

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