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Group analysis of the Novikov equation

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Abstract

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilation symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigate the invariant solutions.

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Acknowledgments

The authors would like to thank FAPESP, São Paulo, Brasil, and BTH, Sweden, for the support giving Nail H. Ibragimov the opportunity to visit IMECC-UNICAMP, where this work was initiated. Yuri Bozhkov would also like to thank FAPESP and CNPq, Brasil, for partial financial support. Igor Leite Freire is thankful to IMECC-UNICAMP for gracious hospitality, UFABC and FAPESP (Grant No. 2011/19089-6) for the financial supports. N. H. Ibragimov’s work is partially supported by the Government of Russian Federation through Resolution No. 220, Agreement No. 11.G34.31.0042.

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Authors and Affiliations

  1. Instituto de Matemática, Estatística e Computação Científica-IMECC, Universidade Estadual de Campinas-UNICAMP, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, 13083-859, Brasil

    Yuri Bozhkov

  2. Centro de Matemática, Computação e Cognição, Universidade Federal do ABC-UFABC, Rua Santa Adélia, 166, Bairro Bangu, Santo André, SP, 09.210-170, Brasil

    Igor Leite Freire

  3. Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, 450000 , Ufa, Russia

    Nail H. Ibragimov

  4. Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 , Karlskrona, Sweden

    Nail H. Ibragimov

Authors
  1. Yuri Bozhkov
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  2. Igor Leite Freire
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  3. Nail H. Ibragimov
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Corresponding author

Correspondence to Igor Leite Freire.

Additional information

Communicated by Eduardo Souza de Cursi.

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Bozhkov, Y., Freire, I.L. & Ibragimov, N.H. Group analysis of the Novikov equation. Comp. Appl. Math. 33, 193–202 (2014). https://doi.org/10.1007/s40314-013-0055-1

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  • DOI: https://doi.org/10.1007/s40314-013-0055-1

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